Question

A group of 3 children and 2 adults pay a total of $120 to take a karate class. A group of 5 children and 1 adult take the same karate class for $95. What is the total cost for 1 child and 1 adult to take the karate class?

Answer 1

The total cost for 1 child and 1 adult to take the karate class is $55.

Step-by-step explanation:

To find the total cost for 1 child and 1 adult to take the karate class, we need to determine the cost per child and the cost per adult.

Let's assume that the cost per child is C and the cost per adult is A.

From the given information, we can set up two equations:

3C + 2A = 120 (equation 1)

5C + A = 95 (equation 2)

To solve this system of equations, we can use the method of substitution or elimination.

Let's solve using substitution:

From equation 2, we can express A in terms of C: A = 95 - 5C

Substitute this into equation 1:

3C + 2(95 - 5C) = 120

Now solve for C:

3C + 190 - 10C = 120

-7C = -70

C = 10

Now substitute C = 10 back into equation 2 to find the cost per adult:

A = 95 - 5C = 95 - 5(10) = 95 - 50 = 45

So, the cost per child is $10 and the cost per adult is $45.

The total cost for 1 child and 1 adult to take the karate class is $10 + $45 = $55.