Question

A group of adults and students went on a class trip to Washington, DC. The number of male students was 1 more than 7 times the number of adults. The number of female students was half the number of male students. If the total number of people who went on the trip is 82, find the numbers of male students and female students. The number of male students is . The number of female students is .

Answer 1

see below

m = males = 50

e = females = 25

a = adults = 7

Explanation:

Givens

Let the adults = a

let the males students = m

lef the female students = e

Equations

a + m + e = 82

m = 7*a + 1

e = 1/2 * (7a + 1)

Solution

a + 7a + 1 + 1/2(7a + 1) = 82 Remove the brackets on the left.

a + 7a + 1 + 3.5*a + 1/2 = 82 Combine the like terms on the left.

11.5a + 1.5 = 82 Subtract 1.5 from both sides.

11.5a + 1.5 - 1.5 = 82 - 1.5 Combine

11.5a = 80.5 Divide by 11.5

a = 80.5/11.5

a = 7

The number of adults = 7

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m = 7a + 1

m = 7*7 + 1

m = 50

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e = 1/2 m

e = 1/2 * 50

e = 25