Question

The cost for 2 adults and 5 children to eat at a local buffet restaurant is $46.50. The cost for 1 adult and 1 child is $15. What is the cost of a child's meal?

Answer 1

$5.50 per child, $9.50 per adult.

Explanation:

We have several pieces of information, but not given "directly" enough to solve the problem in one step. Meaning we need to manipulate our equation a little to solve for our unknowns.

For any equation, you can only have one unknown variable to be able to solve it. In this case, we have two - the price for adult's meal, and the price of the child's meal. We need to rewrite our equation so it only has one unknown.

Let's call A the cost of an adult meal and C the cost of a child meal.

We know from the given information that

`A+C=15`

Also, we know that

`2A+5C=46.50`

Do you see how we have two variables?

Let's solve the first equation for "C"

We simply subtract A from both sides,

`C=15-A`

We now have a value for the variable C! Let's plug that into the other equation!

`2A+5(15-A)=46.50`

Now there is only one variable, A!

Solve for A here by distributing first, then combining like terms, ultimately isolating the variable,

`A=9.50`

This the cost of one adult meal. But we are asked to find the child's meal. No problem. Just plug 9.50 into the first equation, and solve for C.

`C=5.50`

Hope this helped.