Question

The Garza family enrolled their 4-year old, 3-year old, and infant in daycare for $2800 per month. The Martinez family enrolled their 4-year old and twin 3-year olds in the same daycare for $2650 per month. The Richards family spends $3000 per month for their 3-year old and twin infants to attend. Define your variables, and write a system of equations (in the order in which read them) that could be used to solve for the individual cost per child.

A. $x + $y + $z = 2800
B. $x + $2y = 2650
C. $x + 2($y + $z) = 3000
D. $x + $2y + $2z = 3000

Answer 1

The correct system of equations based on the costs of daycare for each family's children is: A. $x + $y + $z = 2800, B. $x + $2y = 2650, and C. $y + 2z = 3000 - $x. These represent individual monthly costs for a 4-year old (x), a 3-year old (y), and an infant (z).

Step-by-step explanation:

The question provided involves creating a system of equations to determine the individual cost per child for daycare. By defining variables x, y, and z for the cost per 4-year old, cost per 3-year old, and cost per infant respectively, we can set up the equations based on the information given for each family's monthly daycare expenditure.

Therefore, the correct system of equations using the information provided is:

1. A. $x + $y + $z = 2800
2. B. $x + $2y = 2650
3. C. $y + 2z = 3000 - $x

The third equation, originally given as option D, needs to be adjusted because $x + $2y + $2z = 3000 is not consistent with the information provided for the Richards family, which shows the cost for a 3-year old and twin infants. Instead, it should be C. $y + 2z = 3000 - $x, where $x is subtracted from $3000 to represent the monthly cost for one 3-year old and twin infants.