Story Problems for systems of equations

1. Applying Systems of
Equations

2. A roadside vegetable stand sells pumpkins for $5 each and squashes for $3 each.
One day they sold 6 more squash than pumpkins, and their sales totaled $98. Write
and solve a system of equations to find how many pumpkins and quash they sold?

3. Anya makes 14 baskets during her game. Some of these baskets
were worth 2 points and others were worth 3 points. In total, she
scored 30 points. Write and solve a system of equations to find
how many 2-point baskets she made.

4. A library contains 2000 books. There are 3 times as many non-
fiction books as fiction books. Write and solve a system of
equations to determine the number of nonfiction and fiction books.

5. The length of a rectangle is three times the width. The sum of the
length and the width is 24 inches. What is the length of the rectangle?

6. An airport shuttle company owns sedans that have a maximum
capacity of 3 passengers and vans that have a maximum capacity of
8 passengers. Their 12 vehicles have a combined maximum capacity
of 61 passengers. How many vans does the company own?

7. Timothy and his brothers are selling lemonade and cookies to raise
funds for a camping trip. Paul bought two cups of lemonade and
two cookies for $3 and Nancy bought three cookies and two cups
of lemonade for $4.00. What is the cost of a cup of lemonade?

8. Veronica has been saving dimes and quarters. She has 94
coins in all, and the total value is $19.30. How many dimes
and how many quarters does she have?

9. Apples
(Ib)
Potatoes
(Ib)
Total Cost
($)
Roger 8 7 18.85
Trevor 2 10 12.88
Roger and Trevor went shopping for produce on the same day.
They each bought some apples and some potatoes. The amount
they bought and the total they paid are listed in the table below.
What was the price per pound of the apples and the potatoes?

10. Concentration
of Solution
Amount of
Solution (L)
Amount
of Acid
15% x
33% y
21% 40
How many liters of 15% acid and 33% acid should be
mixed to make 40 liters of 21% acid solution?

11. The sum of two numbers is 62 and their difference is 8.
What are the two numbers?