I am having trouble creating a table using problem solving

Question

Shasha and Francisco were selling lemonade for .25 cents per half cup and .50 cents per full cup. At the end of the day, they had collected $15 and had used 37 cups. How many full cups and how many half cups did they sell?

Answer 1

Since you specifically mentioned using a table, we can set this problem up with a table instead of a system of equations.

First, make note of what you know.

a half cup (h) costs $0.25

a full cup (f) costs $0.50

They used 37 cups.

Since we know they used exactly 37 cups, we know that h + f = 37

h f $

0 37 $18.50 (since 0*0.25 + 37*0.5=18.5)

1 36 $18.25

2 35 $18.00

3 34 $17.75 (notice a pattern here? every time we shift, we are losing $0.25)

4 33 $17.50

5 32 $17.25

6 31 $17.00

7 30 $16.75

8 29 $16.50

9 28 $16.25

10 27 $16.00

11 26 $15.75

12 25 $15.50

13 24 $15.25

14 23 $15.00

So they sold 14 half cups and 23 full cups to use 37 cups and make $15.00

Double check the answer to make sure it makes sense...

14 x 0.25 = 3.50

23 x 0.50 = 11.50

11.50 + 3.50 = 15.00

Answer 2

h + f = 37 h = 37 - f

.25h + .50 f = 15

Substitute

.25(37 - f) + .50f = 15

9.25 - .25f + .50f = 15

.25f = 7.75

f = 31

h = 6

Plug these back in to check.