Question

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

`25x+15y\geq 1975\\y\leq 4x\\y\geq 50\\x\geq 0`

Explanation:

Let x represents the number of lawns mowed by Mike and y represents the number of cars washed by Beth.

Then, the amount earned by Mike if he charges $25 for moving the lawn
`=25x`

And the amount earned by Beth if she charges $15 for moving the lawn
`=15x`

Then, as need at least $1975 in order to go Disneyworld.

So, first inequality is,

`25x+15y\geq 1975`

Now, it is given that the number of cars that Beth wash is no more than four times the number of lawns Mike has scheduled to mow. So, this gives the inequality,

`y\leq 4x`

Next, it is given that Beth will wash at least 50 cars. So,

`y\geq 50`

Lastly, as the number of lawns mowed can't be negative, so

`x\geq 0`