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Online Quiz (Worksheet A B C D)

Questions Per Quiz = 2 4 6 8 10

Math Word Problems - GED, PSAT, SAT, ACT, GRE Preparation
2.18 Word Problems - Numbers

Example:
One whole number is three times another. Together the numbers add up to 84. Find both numbers.
Let x be the first whole number.
Let 3x be the second whole number.
The two numbers add up to 84 :
x + 3x = 84
4x = 84
x = 21
3x = 63
Therefore the first number is 21 and second number is 63.

Example:
One whole number is three times a second. If 20 is added to the smaller number, the result equals 6 more than the larger number. Find both numbers.
let the smaller number be s and larger number be l
l = 3s
s + 20 = l + 6
s + 20 = 3s + 6
14 = 2s
s = 7
l = 3s = 3x7 = 21

Example:
Separate 45 into two parts such that twice the smaller is 9 less than the larger.
Let x = the smaller part
Let 45 - x = the larger part
twice the smaller is 9 less than the larger:
2(x) = (45-x)- 9
2x = 45 - x - 9
3x = 36
x = 12 which is the smaller part
larger part = 45 - x = 45 - 12 = 33

Directions: Answer the following questions.
Q 1: If 13 less than seven times a whole number is 204, find the number. (Hint: 7x-13 = 204, then x = ____)
43
32
31

Q 2: The larger of two whole numbers is five times the smaller. If the larger number is increased by 3, it equals 15 more than the smaller. find both numbers. (Hint: let x be smaller number, 5x the larger number. If the larger number is increased by 3, it equals 15 more than smaller number: 5x + 3 = x + 15 solve for x and 5x)
smaller number is 2 and larger number is 10
smaller number is 3 and larger number is 15
smaller number is 4 and larger number is 20

Q 3: Separate 15 into two parts such that twice the smaller is 3 more than the larger. (Hint: Let x be the smaller part, then larger part is 15-x. Twice the smaller is three more than the larger: 1(x) = (15 - x) + 3 solve for x and then find the larger number which is 15-x)
smaller number is 7 and larger number is 8
smaller number is 5 and larger number is 10
smaller number is 6 and larger number is 9

Q 4: One whole number is 4 times another. Together the two numbers add up to 100. Find both numbers. (hint: a = 4b, a + b = 100 then a = ? b= ?)
20 and 80
40 and 60
30 and 70

Q 5: One whole number is 12 more than another. If the two numbers add up to 70, find both numbers. (Hint: a = b + 12 , a + b = 70, a= ?, b = ?)
30 and 40
31 and 39
29 and 41

Q 6: The larger of two whole numbers is 7 more than the smaller. Double the smaller number equals 8 more than the larger number. Find both numbers. (Hint: let l be larger number and s be the smaller number. l = 7 + s, 2s = l+8 solve for s and l)
s = 14 and l = 21
s = 13 and l = 20
s = 15 and l = 22

Q 7: Separate 29 into two parts such that three times the smaller is 19 more than the larger. (Hint: let x be the smaller part and 29-x the larger part. 3x = l + 19. Solve for x and 45-x)
smaller number is 9 and larger number = 20
smaller number is 12 and larger number = 17
smaller number is 10 and larger number = 19

Q 8: Five more than three times a whole number is 71. Find the number. (Hint: 3x + 5 = 71 then x = ____)
32
21
22

Question 9: This question is available to subscribers only!

Question 10: This question is available to subscribers only!


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