Question

Help me plz

3.Mike and Beth are saving money to go to Disneyworld. They need at least $1975 in order to go. Mike mows yards and Beth will wash cars to raise money. Mike charges $25 each time he mows a yard and Beth charges $15 for each car she washes. The number of cars that Beth wash is no more than four times the number of lawns Mike has scheduled to mow. Beth will wash at least 50 cars. Write a set of constraints to model the problem, with x representing the number of lawns mowed and y representing the number of dogs walked. Answer:

Answer 1

`\left\{\begin{array}{l}y\le 4x\\y\ge 50\\25x+15y\ge 1975\end{array}\right.`

Explanation:

Let x represent the number of lawns mowed and y represent the number of cars washed.

1. Since the number of cars that Beth wash is no more than four times the number of lawns Mike has scheduled to mow, you have that
`y\le 4x.`.

2. Beth will wash at least 50 cars, then
`y\ge 50.`

3. Mike charges $25 each time he mows a yard, then he earns $25x for mowing x yards. Beth charges $15 for each car she washes, then she earns $15y for y cars washed. They need at least $1975, so

`25x+15y\ge 1975.`

4. A set of constraints to model the problem is

`\left\{\begin{array}{l}y\le 4x\\y\ge 50\\25x+15y\ge 1975\end{array}\right.`