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A group of students from Student Council sold some coupons at their school carnival. There was as many boys as girls in Student Council. Each coupon sold by the boys is $13.20 while each coupon sold by the girls is $10.20. The girls sold $273 worth of coupons more than the boys.(a) How many students were there altogether in Student Council?Answer: (b) How much was the total value of coupons sold by the girls?

Question

A group of students from Student Council sold some coupons at their school carnival. There was as many boys as girls in Student Council. Each coupon sold by the boys is 13.20whileeachcouponsoldbythegirlsis13.20 while each coupon sold by the girls is 10.20. The girls sold $273 worth of coupons more than the boys.(a) How many students were there altogether in Student Council?Answer: (b) How much was the total value of coupons sold by the girls?

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Solution

To solve this problem, we need to set up a system of equations based on the information given in the problem.

Let's denote: B = number of coupons sold by boys G = number of coupons sold by girls

From the problem, we know that:

  1. The number of boys and girls in the Student Council is the same, so the number of coupons sold by boys and girls is the same. Therefore, B = G.
  2. Each coupon sold by the boys is 13.20andeachcouponsoldbythegirlsis13.20 and each coupon sold by the girls is 10.20. Therefore, the total value of coupons sold by boys is 13.20B and the total value of coupons sold by girls is 10.20G.
  3. The girls sold $273 worth of coupons more than the boys. Therefore, 10.20G = 13.20B + 273.

Now we can solve this system of equations.

Substitute B = G into the second equation: 10.20G = 13.20G + 273 Subtract 10.20G from both sides: -3G = 273 Divide both sides by -3: G = -273 / -3 G = 91

Since B = G, B = 91 as well.

(a) The total number of students in the Student Council is B + G = 91 + 91 = 182.

(b) The total value of coupons sold by the girls is 10.20G = 10.20 * 91 = $928.20.

This problem has been solved

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