Question

The equations 8x +4y = 32 and 16x +12y = 72 represent the cost for lunch and dinner for a family eating out on vacation. If x is the number of adults and y is the number of children, how many adults are in the family?

Answer 1

Answer:

There are 3 adults in the family.

Step-by-step explanation:

The equations 8x + 4y = 32 and 16x + 12y = 72 represent the cost of lunch and dinner for a family in which x is the number of adults and y is the number of children.

We have to find the number of adults or the value of x by solving these equations.

equations are 8x + 4y = 32 -------(1)

16x + 12y = 72 --------(2)

Now we will multiply equation 1 by 3 and subtract it by equation 2.

(16x + 12y) -3(8x + 4y) = 72 - 96

16x + 12y - 24x - 12y = -24

(16x - 24x) + (12y - 12y) = -24

-8x = - 24

8x = 24

x = 3

Therefore, there are 3 adults in the family.