Question

A team t-shirt costs $3 per adult and $2 per child. On a certain day, the total number of adults (a) and children (c) who bought shirts was 100, and the total money collected was $275. Which of the following options represents the number of children and the number of adults who purchased team shirts that day, and the pair of equations that can be solved to find the numbers? 75 children and 25 adults Equation 1: a + c = 100 Equation 2: 3a − 2c = 275 75 children and 25 adults Equation 1: a + c = 100 Equation 2: 3a + 2c = 275 25 children and 75 adults Equation 1: a + c = 100 Equation 2: 3a − 2c = 275 25 children and 75 adults Equation 1: a + c = 100 Equation 2: 3a + 2c = 275

Answer 1

3a + 2c = 275  .... t-shirt costs $3 per adult and $2 per child and total money collected was $275

a + c = 100 ... the total number of adults (a) and children (c) who bought shirts was 100

so

3a + 2c = 275
a + c = 100 so a = 100 - c

substitute a =   100 - c into 3a + 2c = 275

3a + 2c = 275
3(100 - c) + 2c = 275
300 - 3c + 2c = 275
-c = - 25
c = 25
a = 100 -c = 100 - 25 = 75

so a = 75 (adults) and c = 25 (children)

answer

Equation 1: a + c = 100
Equation 2: 3a + 2c = 275
25 children and 75 adults

Answer 2

I did this problem before so if im correct, this is the solution

 a = 75 (adults) and c = 25 (children)
Equation 1: a + c = 100 
Equation 2: 3a + 2c = 275