Question

Two cooks purchased plates and cups at the same store. The first cook bought 4 plates and 5 cups for a total of $25.25. The second cook bought 7 plates and 3 cups for a total of $25.50.

What is the price of a plate?

Answer 1

I am unsure on how to solve this question.

Answer 2

Let p represent the price of one plate
and c represent the price of one cup

Then the total price of cups and plates purchased by the 1st cook is represented by
4p + 5c = 25.25

And the total price of cups and plates purchased by the 2nd cook is represented by
7p + 3c = 25.50



In other words we have to solve the following system for p:
4p + 5c = 25.25
7p + 3c = 25.50

Answer 3

The amount of p and c has to be the same in both equations right?

Answer 4

I'm pretty confident you already know the answer to that question.

Answer 5

Just making sure.

Answer 6

Hero is there a faster way to do it instead of choosing random numbers for p then trying to see if they work?

Answer 7

you can use elimination. try multiplying the first equation by 3 and the second equation by 5 and let me know what you get

Answer 8

the entire equation? like 4p+5c=25.25 (5)

Answer 9

first equation *3
second equation * 5, so:

[ 4p+5c=25.25 ] * (3)
[ 7p + 3c = 25.50 ] * (5)

now try distributing the 3 and 5

Answer 10

12p+15c=75.75

Answer 11

35p+15c=127.5

Answer 12

good, now subtract equation 2 - equation 1

35p - 12p = ?
15c - 15c = ?
127.5 - 75.75 = ?

Answer 13

23p=51.75

Answer 14

good, so p = ?

Answer 15

2.25

Answer 16

:o thanks cx

Answer 17

good, so plate = $2.25 = your answer