Algebra 1 word problem

Question

Trevon and Eduardo are selling pies for a school fundraiser. Customers can buy cherry pies and lemon meringue pies. Trevon sold 9 cherry pies and 4 lemon meringue pies for a total of $104. Eduardo sold 6 cherry pies and 6 lemon meringue pies for a total of $126. What is the cost each of one cherry pie and one lemon meringue pie? 

Answer 1

Here's another (popular) system of equations problem.

Let C = price of cherry pie; L = price of lemon pie. Money from sale = No. pies x price/pie.

For Trevon: 9C + 4L = $104

For Eduardo: 6C + 6L = $126 Need to eliminate one of the variables. Can use substitution by manipulating one of the equations to isolate a variable and inserting the result into the other, or elimination. For this problem I would choose the latter.

One way would be to multiplty the 1st eqn by 3 and the 2nd by -2. This will eliminate the "L" variable.

3(9C + 4L ) = 3(104) -> 27C + 12L = 312

-2(6C + 6L) = -2(126) -> -12C - 12L = -252 Now can add.

15C = 60 C = $4

Now substitute into one of the eqns to find L: 9(4) + 4L = 104 -> 36 + 4L = 104 -> 4L = 68 L = $17

Check: 9(4) + 4(17) = 104? (Yes)

6(4) + 6(17) = 126? (Yes) I'm wondering why lemon pie costs so much more!!

Answer 2

Always start algebra word problems like this by assigning variables. Let's use y for cherry pies and x for lemon meringue. (You can use any two letters, but using x and y will allow you to graph them with a tool like Desmos.com.)

That said, you can solve this by graphing them and finding the point of intersection or by solving the "system of equations" you write.

Since y=cherry and x=lemon meringue, we can write:

9x+4y=104 and 6x+6y=126. You can solve these with substitution or elimination, and since all the numbers in the second equation are divisible by 6, I chose substitution. Here's how:

Divide all terms of 6x+6y=126 by 6 to get x+y=21.

Subtract y from both sides to get x=21-y.

Substitute the new expression for x into the other, initial equation:

9(21-y)+4y = 104

189-9y+4y = 104

189-5y=104

-5y=-20

y=4

So cherry pies are $4 each. Plug this back into either initial equation to find the cost of lemon meringue pies: 6x+6(4)=126

6x+24=126

6x=102

x=$17

If you graph these, you'll find the intersection point at (17,4).

I hope this helps, and have fun mathing!

Liz Z.