Systems By Substitution

Question

Swimming Pool On a certain hat summer's day, 637 people used the public swimming pool. The cally prices are $1.75 for children and $2.50 for adults. The reipts for admission totaled $130975 How many children and how many adus vam at the public pool that day?

Answer 1

Request was for substitution (not elimination) method.

C + A = 637, so C = 637 - A

1.75C + 2.50 A = 1309.75

Substituting: 1.75(637 - A) + 2.50A = 1309.75

1114.75 - 1.75A + 2.50A = 1309.75

Combining like terms, etc. 0.75A = 195 → A = 195/0.75 → A = 260 Adults

C = 637 - 260 = 377 Children

Answer 2

C is children. A is adults.

C + A = 637

1.75C + 2.50A = 1309.75

Multiply the first equation by -1.75. Subtract it from the second equation.

1.75C + 2.50A = 1309.75

-1.75C - 1.75A = -1.75 * 637

.75 A = 1309.75 - 1114.75 = 195

A = 195/.75 = 260

C = 637 - 260 = 377