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# C1 c2-workback

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### C1 c2-workback

1. 1. <ul><li>Timothy had some watermelons. He gave half of his watermelons to David. David then gave half of his oranges to Timothy. Timothy sold 8 watermelons and David sold 32 oranges. In the end, the ratio of watermelons to oranges for Timothy and David is 1:5 and 1:3 respectively. How many watermelons did Timothy have at first? </li></ul>C1 – C2 Work backwards
2. 2. <ul><li>Timothy had some watermelons. He gave half of his watermelons to David. David then gave half of his oranges to Timothy. Timothy sold 8 watermelons and David sold 32 oranges. In the end, the ratio of watermelons to oranges for Timothy and David is 1:5 and 1:3 respectively. How many watermelons did Timothy have at first? </li></ul>Step 1 Case 1:Timothy C1 – C2 Work backwards Case 2: David After Change 0 O W Before ? Change ÷2 After Change After O W Before Change +? After
3. 3. <ul><li>Timothy had some watermelons. He gave half of his watermelons to David. David then gave half of his oranges to Timothy. Timothy sold 8 watermelons and David sold 32 oranges. In the end, the ratio of watermelons to oranges for Timothy and David is 1:5 and 1:3 respectively. How many watermelons did Timothy have at first? </li></ul>Step 1 Case 1:Timothy Case 2: David Step 2 C1 – C2 Work backwards After Change +? 0 O W Before ? Change ÷2 After Change After ÷2 ? O W Before 0 Change +? After
4. 4. <ul><li>Timothy had some watermelons. He gave half of his watermelons to David. David then gave half of his oranges to Timothy. Timothy sold 8 watermelons and David sold 32 oranges. In the end, the ratio of watermelons to oranges for Timothy and David is 1:5 and 1:3 respectively. How many watermelons did Timothy have at first? </li></ul>Step 1 Case 1:Timothy Case 2: David Step 2 Step 3 C1 – C2 Work backwards After – 8 Change +? 0 O W Before ? Change ÷2 After – 32 Change After ÷2 ? O W Before 0 Change +? After
5. 5. <ul><li>Timothy had some watermelons. He gave half of his watermelons to David. David then gave half of his oranges to Timothy. Timothy sold 8 watermelons and David sold 32 oranges. In the end, the ratio of watermelons to oranges for Timothy and David is 1:5 and 1:3 respectively. How many watermelons did Timothy have at first? </li></ul>Step 1 Case 1:Timothy Case 2: David Step 2 Step 3 C1 – C2 Work backwards After – 8 Change 5u +? 0 O W Before ? Change ÷2 After 1u – 32 Change After 3p ÷2 ? O W Before 0 Change +? After 1p
6. 6. <ul><li>Timothy had some watermelons. He gave half of his watermelons to David. David then gave half of his oranges to Timothy. Timothy sold 8 watermelons and David sold 32 oranges. In the end, the ratio of watermelons to oranges for Timothy and David is 1:5 and 1:3 respectively. How many watermelons did Timothy have at first? </li></ul>Step 1 Case 1:Timothy Case 2: David Step 2 Step 3 Step 4 C1 – C2 Work backwards 5u 1u+8 After – 8 Change 5u +? 0 O W Before ? Change ÷2 After 1u – 32 Change 3p+32 1p After 3p ÷2 ? O W Before 0 Change +? After 1p
7. 7. <ul><li>Timothy had some watermelons. He gave half of his watermelons to David. David then gave half of his oranges to Timothy. Timothy sold 8 watermelons and David sold 32 oranges. In the end, the ratio of watermelons to oranges for Timothy and David is 1:5 and 1:3 respectively. How many watermelons did Timothy have at first? </li></ul>Step 1 Case 1:Timothy Case 2: David Step 2 Step 3 Step 4 C1 – C2 Work backwards 5u 1u+8 After – 8 Change 5u +? 0 O W Before 2u+16 Change ÷2 After 1u – 32 Change 3p+32 1p After 3p ÷2 ? O W Before 0 Change +? After 1p
8. 8. <ul><li>Timothy had some watermelons. He gave half of his watermelons to David. David then gave half of his oranges to Timothy. Timothy sold 8 watermelons and David sold 32 oranges. In the end, the ratio of watermelons to oranges for Timothy and David is 1:5 and 1:3 respectively. How many watermelons did Timothy have at first? </li></ul>Step 1 Case 1:Timothy Case 2: David Step 2 Step 3 Step 4 C1 – C2 Work backwards 5u 1u+8 After – 8 Change 5u +? 0 O W Before 2u+16 Change – (1u+8) After 1u – 32 Change 3p+32 1p After 3p ÷2 ? O W Before 0 Change +? After 1p
9. 9. <ul><li>Timothy had some watermelons. He gave half of his watermelons to David. David then gave half of his oranges to Timothy. Timothy sold 8 watermelons and David sold 32 oranges. In the end, the ratio of watermelons to oranges for Timothy and David is 1:5 and 1:3 respectively. How many watermelons did Timothy have at first? </li></ul>Step 1 Case 1:Timothy Case 2: David Step 2 Step 3 Step 4 C1 – C2 Work backwards 5u 1u+8 After – 8 Change 5u +? 0 O W Before 2u+16 Change – (1u+8) After 1u – 32 Change 3p+32 1p After 3p ÷2 ? O W Before 0 Change +(1u+8) After 1p
10. 10. <ul><li>Timothy had some watermelons. He gave half of his watermelons to David. David then gave half of his oranges to Timothy. Timothy sold 8 watermelons and David sold 32 oranges. In the end, the ratio of watermelons to oranges for Timothy and David is 1:5 and 1:3 respectively. How many watermelons did Timothy have at first? </li></ul>Step 1 Case 1:Timothy Case 2: David Step 2 Step 3 Step 4 C1 – C2 Work backwards 5u 1u+8 After – 8 Change 5u +? 0 O W Before 2u+16 Change – (1u+8) After 1u – 32 Change 3p+32 1p After 3p ÷2 6p+64 O W Before 0 Change +(1u+8) After 1p
11. 11. <ul><li>Timothy had some watermelons. He gave half of his watermelons to David. David then gave half of his oranges to Timothy. Timothy sold 8 watermelons and David sold 32 oranges. In the end, the ratio of watermelons to oranges for Timothy and David is 1:5 and 1:3 respectively. How many watermelons did Timothy have at first? </li></ul>Step 1 Case 1:Timothy Case 2: David Step 2 Step 3 Step 4 C1 – C2 Work backwards 5u 1u+8 After – 8 Change 5u +? 0 O W Before 2u+16 Change – (1u+8) After 1u – 32 Change 3p+32 1p After 3p – (3p+32) 6p+64 O W Before 0 Change +(1u+8) After 1p
12. 12. <ul><li>Timothy had some watermelons. He gave half of his watermelons to David. David then gave half of his oranges to Timothy. Timothy sold 8 watermelons and David sold 32 oranges. In the end, the ratio of watermelons to oranges for Timothy and David is 1:5 and 1:3 respectively. How many watermelons did Timothy have at first? </li></ul>Step 1 Case 1:Timothy Case 2: David Step 2 Step 3 Step 4 C1 – C2 Work backwards 5u 1u+8 After – 8 Change 5u +(3p+32) 0 O W Before 2u+16 Change – (1u+8) After 1u – 32 Change 3p+32 1p After 3p – (3p+32) 6p+64 O W Before 0 Change +(1u+8) After 1p
13. 13. <ul><li>Timothy had some watermelons. He gave half of his watermelons to David. David then gave half of his oranges to Timothy. Timothy sold 8 watermelons and David sold 32 oranges. In the end, the ratio of watermelons to oranges for Timothy and David is 1:5 and 1:3 respectively. How many watermelons did Timothy have at first? </li></ul>Step 1 Case 1:Timothy Case 2: David Step 2 Step 3 Step 4 C1 – C2 Work backwards 5u  3p + 32 1p  1u+8 5u 1u+8 After – 8 Change 5u +(3p+32) 0 O W Before 2u+16 Change – (1u+8) After 1u – 32 Change 3p+32 1p After 3p – (3p+32) 6p+64 O W Before 0 Change +(1u+8) After 1p
14. 14. <ul><li>Timothy had some watermelons. He gave half of his watermelons to David. David then gave half of his oranges to Timothy. Timothy sold 8 watermelons and David sold 32 oranges. In the end, the ratio of watermelons to oranges for Timothy and David is 1:5 and 1:3 respectively. How many watermelons did Timothy have at first? </li></ul>Step 1 Case 1:Timothy Case 2: David Step 2 Step 3 Step 4 C1 – C2 Work backwards 5u  3p + 32 1p  1u+8 3p  3u + 24 5u 1u+8 After – 8 Change 5u +(3p+32) 0 O W Before 2u+16 Change – (1u+8) After 1u – 32 Change 3p+32 1p After 3p – (3p+32) 6p+64 O W Before 0 Change +(1u+8) After 1p
15. 15. <ul><li>Timothy had some watermelons. He gave half of his watermelons to David. David then gave half of his oranges to Timothy. Timothy sold 8 watermelons and David sold 32 oranges. In the end, the ratio of watermelons to oranges for Timothy and David is 1:5 and 1:3 respectively. How many watermelons did Timothy have at first? </li></ul>Step 1 Case 1:Timothy Case 2: David Step 2 Step 3 Step 4 C1 – C2 Work backwards 3p 32 5u 5u  3p + 32 1p  1u+8 3p  3u + 24 5u 1u+8 After – 8 Change 5u +(3p+32) 0 O W Before 2u+16 Change – (1u+8) After 1u – 32 Change 3p+32 1p After 3p – (3p+32) 6p+64 O W Before 0 Change +(1u+8) After 1p
16. 16. <ul><li>Timothy had some watermelons. He gave half of his watermelons to David. David then gave half of his oranges to Timothy. Timothy sold 8 watermelons and David sold 32 oranges. In the end, the ratio of watermelons to oranges for Timothy and David is 1:5 and 1:3 respectively. How many watermelons did Timothy have at first? </li></ul>Step 1 Case 1:Timothy Case 2: David Step 2 Step 3 Step 4 C1 – C2 Work backwards 3p 32 5u 3u 24 5u  3p + 32 1p  1u+8 3p  3u + 24 5u 1u+8 After – 8 Change 5u +(3p+32) 0 O W Before 2u+16 Change – (1u+8) After 1u – 32 Change 3p+32 1p After 3p – (3p+32) 6p+64 O W Before 0 Change +(1u+8) After 1p
17. 17. <ul><li>Timothy had some watermelons. He gave half of his watermelons to David. David then gave half of his oranges to Timothy. Timothy sold 8 watermelons and David sold 32 oranges. In the end, the ratio of watermelons to oranges for Timothy and David is 1:5 and 1:3 respectively. How many watermelons did Timothy have at first? </li></ul>Step 1 Case 1:Timothy Case 2: David Step 2 Step 3 Step 4 C1 – C2 Work backwards 3p 32 5u 3u 24 5u  3p + 32 1p  1u+8 3p  3u + 24 5u 1u+8 After – 8 Change 5u +(3p+32) 0 O W Before 2u+16 Change – (1u+8) After 1u – 32 Change 3p+32 1p After 3p – (3p+32) 6p+64 O W Before 0 Change +(1u+8) After 1p 32 5u 2u=32+24 3u 24
18. 18. <ul><li>Timothy had some watermelons. He gave half of his watermelons to David. David then gave half of his oranges to Timothy. Timothy sold 8 watermelons and David sold 32 oranges. In the end, the ratio of watermelons to oranges for Timothy and David is 1:5 and 1:3 respectively. How many watermelons did Timothy have at first? </li></ul>Step 1 Case 1:Timothy Case 2: David Step 2 Step 3 Step 4 Step 4 5u  3p + 32 1p  1u+8 3p  3u + 24 2u  56 56 + 16 = 72 3p Ans: 72 C1 – C2 Work backwards 5u 1u+8 After – 8 Change 5u +(3p+32) 0 O W Before 2u+16 Change – (1u+8) After 1u – 32 Change 3p+32 1p After 3p – (3p+32) 6p+64 O W Before 0 Change +(1u+8) After 1p 32 5u 2u=32+24 3u 24