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?

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

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

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

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

Answer 1

The answer is:

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

Have a nice day!

Answer 2

Option D is correct.

Explanation:

A team t-shirt costs $3 per adult and $2 per child.

Let the number of children be = c

Let the number of adults be = a

A team t-shirt costs $3 per adult that is 3a and $2 per child that is 2c, also given is that the total money collected is $275, so equation becomes:

`3a+2c=275`

On a certain day, the total number of adults (a) and children (c) who bought shirts was 100, equation becomes:
`a+c=100`

Now to know the number of children and adult, we can check by plugging in the values from options provided.

25 children and 75 adults = 25(2)+75(3)=50+225 =275

Rest options do not fulfill the requirements, so Option D is correct.