Regina, Phil, and joseph each wrote expressions to represent their hourly earnings from an after-school job where h represents the number of hours worked.
Regina: 6.50h + 16
Phil: 3(2.5h+5)
Joseph: 7.50h+10
How many hours will phil and joseph have to work in order to make the same amount of money in one week? explain.
To find out how many hours Phil and Joseph will have to work in order to make the same amount of money in one week, we need to set both of their expressions equal to each other and solve for h.
Setting Phil's expression equal to Joseph's expression, we have:
3(2.5h+5) = 7.50h+10
Expanding the left side of the equation, we have:
7.5h + 15 = 7.5h + 10
The 7.5h term cancels out on both sides of the equation, leaving us with:
15 = 10
This equation is not true, which means that there is no solution. Therefore, Phil and Joseph cannot make the same amount of money in one week, regardless of the number of hours they work.
To find the number of hours Phil and Joseph will have to work in order to make the same amount of money in one week, we need to set their earnings expressions equal to each other.
Phil's earnings expression: 3(2.5h+5)
Joseph's earnings expression: 7.50h+10
Setting them equal to each other, we get:
3(2.5h+5) = 7.50h+10
First, let's simplify Phil's expression:
3(2.5h+5) = 7.5h + 15
Now we have:
7.5h + 15 = 7.5h + 10
Notice that both sides of the equation have 7.5h on them. We can subtract 7.5h from both sides to cancel it out:
7.5h - 7.5h + 15 = 7.5h - 7.5h + 10
This simplifies to:
15 = 10
However, we can see that 15 does not equal 10, which means there is no value of h that will make Phil and Joseph earn the same amount of money in one week.
Therefore, Phil and Joseph will not be able to make the same amount of money in one week, regardless of the number of hours they work.