Multiplying and dividing fractions and mixed numbers

Question

of the total of the spectators at a circus show, 1/4 are men, 2/5 are the remaining number of spectators are women. There are 132 women at the circus show. How many children are at the circus show?

 

Multiplying and dividing fractions and mixed numbers

Answer 1

Hi Steve,

 

First we need variables for our unknowns. I'm going to let M = number of men, W = number of women, C = number of children, and T = total number of spectators. Second we need to translate the given information into manageable formulas. This word problem is bad / a little bit tricky though, because of the way they worded "2/5 of the remaining number of spectators are women." This is going to be tricky to translate. Here are our formulas:

 

• T = M + W + C (Total number = men + women + children)
• T / 4 = M (1/4 of the spectators are men)
• W = 132 (given)
• (2/5) (T - M) = W (2/5 of the *remaining* number of spectators are women. This means after we substract the men from the total, (T-M), 2/5 of that value is = W)

 

Okay so now we need to do some substitutions and solve for C:

 

• W = (2/5)(T - M)
• 132 = (2/5) (T - (T/4))
• 132 = (2/5) (3T / 4)
• 132 = 6T / 20 = 3T / 10
• 132 = 3T / 10
• 1320 = 3T
• T = 440

 

Thus:

 

• M = 440 / 4 = 110
• T = M + W + C
• 440 = 110 + 132 + C
• 440 = 242 + C
• C = 198

 

There are 198 children at the circus show.

Hope this helps!