Olivia had 6 times as much money as Michael. After Olivia spent
13 of her money and Michael spent
45 of his money, they had a total of $1428 left.
- How much money did Olivia and Michael have altogether at first?
- Michael spent 45 of his remaining money on a sweater. What fraction of his original amount of money did he spend on the sweater?
| |
Olivia |
Michael |
Total |
| Before |
6 u |
1 u |
|
| Change |
- 2 u |
- 0.8 u |
|
| After |
4 u |
0.2 u |
$1428 |
(a)
Amount that Olivia spent
=
13 x 6 u
= 2 u
Amount that Michael spent
=
45 x 1 u
= 0.8 u
Amount that Olivia and Michael spent
= 2 u + 0.8 u
= 4.2 u
4.2 u = 1428
1 u = 1428 ÷ 4.2 = 340
Amount that Olivia and Michael had altogether at first
= 6 u + 1 u
= 7 u
= 7 x 340
= $2380
(b)
Amount that Michael spent on the sweater
=
45 x 0.2 u
= 0.16 u
Fraction of Michael's original amount that he spent on a sweater
=
0.161 =
0.16 x 1001 x 100=
16100=
425 Answer(s): (a) $2380; (b)
425 
