number problems. consecutive integers problems. digit problems. geometry problems. age problems. money problems. investment problems. mixture problems. motion problems. work problems

1. I. Number Problems
1. The sum of three positive numbers is 33. The second number is 3 greater than the first
and the third is 4 times the first. Find the three numbers.
2. The sum of three positive numbers is 24. The second number is 4 greater than the first
and the the third is 3 times the first. Find the three numbers.
3. One number exceeds another number by 5. If the sum of the two numbers is 39, Find
the smaller number.
II. Consecutive Integer Problems
1. The sum of the least and greatest of 3 consecutive integers is 60. Find the integers.
2. The sum of three consecutive integers is 24. Find the integers.
3. The sum of four consecutive odd integers is 464. What is the product of the second
and third integers?
III. Digit Problems
1. The digit at the ten’s place of a two digit number is twice the digit at the unit’s place. If
the sum of this number and the number formed by reversing the digits is 66. Find the
number .
2. The sum of digits of two digit number is 12. If the new number formed by reversing
the digits is less than the original number by 54 .Find the original number.
3. The sum of a two digit number and the number obtained by reversing the order of the
digit is 165. If the digits are differ by 3, find the original number.
IV. Geometry Problems
1. A triangle has a perimeter of 50. If 2 of its sides are equal and the third side is 5 more
than the equal sides, what is the length of the third side?
2. The width of a rectangle is 3 feet less than its length. The perimeter of the rectangle is
110 feet. Find its dimensions.
3. In a quadrilateral two angles are equal. The third angle is equal to the sum of the two
equal angles. The fourth angle is 60° less than twice the sum of the other three angles.
Find the measures of the angles in the quadrilateral.
V. Age Problems
1. Five years ago, Mae’s age was half of the age he will be in 8 years. How old is he
now?
2. John is twice as old as his friend Peter. Peter is 5 years older than Alice. In 5 years,
John will be three times as old as Alice. How old is Peter now?
3. Jay’s father is 5 times older than Jay and Jay is twice as old as his sister Mae. In two years
time, the sum of their ages will be 58. How old is Jay now?
VI. Money Problems
1. Paul has 31.15 from paper route collections. He has 5 more nickels than quarters and₱
7 fewer dimes than quarters. How many of each coin does Paul have?
2. Terri has $13.45 in dimes and quarters. If there are 70 coins in all, how many of each
coin does she have?

2. 3. Bobbie has $1.54 in quarters, dimes, nickels, and pennies. He has twice as many dimes
as quarters and three times as many nickels as dimes. The number of pennies is the same
as the number of dimes. How many of each coin does he have?
VII. Investment Problems
1. A woman had 10,000 to invest. She deposited her money into two accounts—one₱
paying 6% interest and the other 71
/2 interest. If at the end of the year the total interest
earned was 682.50, how much was originally deposited in each account?₱
2. A church congregation has 20,000 to be invested in a fund, part at 3% and part at 7%.₱
If the investment at 7% earns 500 more per year than the other placement, how much is₱
invested at each rate?
3. An investment of $3,000 is made at an annual simple interest rate of 5%. How much
additional money must be invested at an annual simple interest rate of 9% so that the total
annual interest earned is 7.5% of the total investment?
VIII. Mixture Problems
1. Coffee worth $1.05 per pound is mixed with coffee worth 85¢ per pound to obtain 20
pounds of a mixture worth 90¢ per pound. How many pounds of each type are used?
2. Solution A is 50% hydrochloric acid, while solution B is 75% hydrochloric acid. How
many liters of each solution should be used to make 100 liters of a solution which is 60%
hydrochloric acid?
3. A tank has a capacity of 10 gallons. When it is full, it contains 15% alcohol. How
many gallons must be replaced by an 80% alcohol solution to give 10 gallons of 70%
solution?
IX. Work Problems
1. Jairus can mow the lawn in 40 minutes and Reuel can mow the lawn in 60 minutes.
How long will it take for them to mow the lawn together?
2. Jane, Lei and Shar can finish painting the fence in 2 hours. If Jane does the job alone she can
finish it in 5 hours. If Lei does the job alone he can finish it in 6 hours. How long will it take for
Shar to finish the job alone?
3. If 6 workers can harvest a field in 18 hours, how many workers would it have taken to
do it in 3 hours?
X. Motion Problems
1. Mike and Philip who live 14 miles apart start at noon to walk toward each other at
rates of 3 mph and 4 mph respectively. In how many hours will they meet?
2. In still water, Finn’s boat goes 4 times as fast as the current in the river. He takes a 15-
mile trip up the river and returns in 4 hours. Find the rate of the current.
3. How long will it take a bus traveling 72 km/hr to go 36 km?