Jerod started the night with $5 in his pocket and earns an average of $2 per pizza delivery in tips. Henry earns an average of $3 per pizza delivery in tips. How many deliveries must they both make in order to have the same amount of money?

Question

Jerod started the night with $5 in his pocket and earns an average of $2 per pizza delivery in tips. Henry earns  an average of $3 per pizza delivery in tips. How many deliveries must they both make in order to have the same amount of money?

Julia Adams · Accepted Answer

They must each make 5 deliveries in order to have the same amount of money.

Let's let #d# be the number of deliveries each person makes. We know that Jared starts with #5#, so that's a constant. However, he also makes #$2# per delivery, or #2d#. So the expression is #5 + 2d#. Henry makes #$3# per delivery but starts with no money, so that becomes #3d#. To find the number of deliveries they must both make to have the same amount of money, we make the two expressions equal to each other and solve for #n#: #5 + 2d = 3d# To solve for #d#, we have to isolate it (make it by itself). To do so, first subtract #color(blue)(2d)# from both sides of the equation: #5 + 2d quadcolor(blue)(-quad2d) = 3d quadcolor(blue)(-quad2d)# #5 = d# or #d = 5# To have the same amount of money, they must each make five deliveries. I hope this is useful.

Isaiah Anthony · Answer

undefined Jerod earns $2 per delivery, and Henry earns $3 per delivery. To find out how many deliveries they must both make to have the same amount of money, we need to set up an equation. Let $x$ be the number of deliveries they both make. Jerod will have $5 + 2x$ dollars, and Henry will have $3x$ dollars. Setting these two expressions equal to each other gives:

$$5 + 2x = 3x$$

Solving for $x$:

$$5 = 3x - 2x$$
$$5 = x$$

Therefore, they both must make 5 deliveries to have the same amount of money.