The equation for:
Judy and Linda agree to share the cost
of a $21 pizza based on how much each one ate. If Judy ate 3/4 of the amount that Linda ate, how much should each pay?
what is the formula please.
if Linda paid x, then Judy should pay 3/4 x
Add it all together to get the whole cost:
x + 3/4 x = 21
7/4 x = 21
x = 21 * 4/7 = 12
So, Linda paid $12, Judy paid $9
To find out how much each person should pay, we need to use the concept of proportions.
Let's assume that Linda ate x amount of the pizza. Since Judy ate 3/4 of the amount that Linda ate, Judy must have eaten (3/4) * x amount of the pizza.
Now, let's assign variables to the amount each person should pay. Let's say Judy will pay J dollars, and Linda will pay L dollars.
Since the total cost of the pizza is $21, we can say that J + L = $21.
Now, we need to express the proportion of how much each person ate in terms of the money they should pay. The proportion can be expressed as:
Judy's share / Linda's share = J / L = Judy's portion of pizza / Linda's portion of the pizza
Since Judy ate (3/4) * x and Linda ate x, the proportion becomes:
J / L = (3/4) * x / x
Now, simplify the proportion:
J / L = 3/4
Cross-multiplying, we get:
4J = 3L
Now, substitute J + L = $21 into the equation:
4J = 3(21 - J)
Simplify:
4J = 63 - 3J
Combine like terms:
7J = 63
Divide both sides by 7:
J = 9
Now, substitute the value of J back into J + L = $21:
9 + L = 21
Subtract 9 from both sides:
L = 12
Therefore, Judy should pay $9, and Linda should pay $12.
To determine how much each person should pay, we need to set up a proportion based on the amount each person ate. Let's denote the amount Linda ate as "L" and the amount Judy ate as "J".
Given that Judy ate 3/4 of the amount that Linda ate, we can write the equation:
J = (3/4)L
Now, let's assign a variable for the amount each person pays. Let "Jp" be the amount Judy pays and "Lp" be the amount Linda pays.
Since Judy and Linda will share the cost of a $21 pizza, the equation can be written as:
Jp + Lp = $21
To solve this system of equations, we need to substitute J in terms of L into the second equation:
(3/4)L + Lp = $21
Simplifying the equation, we multiply both sides by 4 to eliminate the fraction:
3L + 4Lp = $84
Now we have two equations:
J = (3/4)L
3L + 4Lp = $84
These equations can be used to find the values of Lp and Jp, which represent the amount each person should pay.