Problems

Question 1

There are four more women than men on Centerville’s board of education. If there are ten members on the board, how many are women?

Answer 1

Variables: men = m, women = w
Equations: w = m + 4, m + w = 10
Combine and Solve:
m + (m + 4) = 10 
2m + 4 = 10 
2m = 6 
m = 3
w = (3) + 4 w = 7

Question 2

If Sam were twice as old as he is, he would be 40 years older than Jim. If Jim is 10 years younger than Sam, how old is Sam?

Answer 2

Variables: Sam = s, Jim = j
Equations: 2s = j + 40, j = s – 10
Combine and Solve:
2s = (s – 10) + 40 
2s = s + 30 
s = 30
j = (30) – 10 j = 20

Question 3

The average of 10, 30, and 50 is 5 more than the average of x, 20, and 40. What number is x?

Answer 3

Variables: x
Equations: (10+30+50)/3 = [(x+20+40)/3]+5
Combine and Solve:
(10+30+50)/3 = [(x+20+40)/3]+5
(10+30+50) = (x+20+40) + 15
90 = x + 75
15 = x

Question 4

25% of the students at a high school attended the pep rally. If there are 600 students total, how many students did not attend the pep rally?

Answer 4

Variables: total students = t
Solve: If 25% of the students attended the pep rally, then 75% of the students did not attend.
75% of 600 = 0.75 × 600 = 450

Question 5

After taxes, Sally keeps 4/5 of her gross pay. If her monthly taxes are $1400, what is her monthly gross pay?

Answer 5

Variables: gross pay = g
Solve: If she keeps 4/5 of her gross pay, that means that taxes represent 1/5 of her gross pay.
1,400 = (1/5)g
7,000 = g

Question 6

Two jars that are both half full of liquid are poured into an empty bucket. If the bucket has three times the capacity of each jar, what portion of the bucket is now full?

Answer 6

If the jars are half full, then they each have 1 unit of liquid.
If each is poured into the bucket, the bucket will have 2 units of liquid.
That means the bucket is 2/6 = 1/3 full of liquid.

Question 7

As a salesperson, Phyllis can choose one of two methods of annual payment: either an annual salary of $35,000 with no commission or an annual salary of $10,000 plus a 20 percent commission on her total annual sales. What must her total annual sales be to give her the same annual pay with either method?

Answer 7

Variables: total annual sales = s
Solve: For the pay to eb the same, we need to set the two amounts equal to each other. We can
represent the amount made with commission as 10,000 + 0.2s
35,000 = 10,000 + 0.2s
25,000 = 0.2s
125,000 = s