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

To find the number of adults in the family, we need to solve the system of equations. By multiplying the first equation by 2 and subtracting it from the second equation, we can eliminate x and solve for y. Substituting the value of y back into the first equation, we can solve for x. The number of adults in the family is 3.

Step-by-step explanation:

To find the number of adults in the family, we need to solve the system of equations:

Equation 1: 8x + 4y = 32

Equation 2: 16x + 12y = 72

We can solve this system by first multiplying Equation 1 by 2 to make the coefficients of x in both equations the same. This gives us:

Equation 1 (multiplied by 2): 16x + 8y = 64

Next, we can subtract Equation 1 (multiplied by 2) from Equation 2 to eliminate x:

Equation 2 - Equation 1 (multiplied by 2): (16x + 12y) - (16x + 8y) = 72 - 64

Simplifying the equation, we get:

4y = 8

Dividing both sides by 4, we find:

y = 2

So, there are 2 children in the family. Substituting this value back into Equation 1, we can solve for x:

8x + 4(2) = 32

8x + 8 = 32

8x = 24

Dividing both sides by 8, we find:

x = 3

Therefore, there are 3 adults in the family.

Answer 2

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.