Kathy and Diana had $196. Diana had $16 more than Kathy. Kathy spent 3 times as much as Diana and was left with
35 as much as Diana. How much did Kathy spend?
| |
Make p the same
(1)x5 = (3) |
Kathy
(1) |
Diana
(2) |
Make p the same
(2)x3 = (4) |
Total
|
Comparing Kathy
and Diana at first |
|
|
$16 more |
|
$196 |
| Before |
$450 |
$90 |
$106 |
$318 |
|
| Change |
- 15 u |
- 3 u |
- 1 u |
- 3 u |
|
| After |
15 p |
3 p |
5 p |
15 p |
|
Amount that Kathy had at first
= (196 - 16) ÷ 2
= 180 ÷ 2
= $90
Amount that Diana had at first
= 90 + 16
= $106
90 - 3 u = 3 p --- (1)
106 - 1 u = 5 p --- (2)
Make p the same.
(1)
x 5
450 - 15 u =
15 p --- (3)
(2)
x 3
318 - 3 u =
15 p --- (4)
(4) = (3)
318 - 3 u = 450 - 15 u
15 u - 3 u = 450 - 318
12 u = 132
1 u = 132 ÷ 12 = 11
Amount that Kathy spent
= 3 u
= 3 x 11
= $33
Answer(s): $33
