Ivan and Michael were given some allowances each. If Ivan spent $11 each day and Michael spent $33 each day, Ivan would still have $2059 left when Michael spent all his allowance. If Ivan spent $33 each day and Michael spent $11 each day, Ivan would still have $35 left when Michael spent all his allowance.
- How much allowance did Ivan receive?
- How much allowance did Michael receive?
|
Case 1 |
Case 2 |
|
Ivan |
Michael |
Ivan |
Michael |
Before |
1 u + 2059 |
3 u |
3 p + 35 |
1 p |
Change |
- 1 u |
- 3 u |
- 3 p |
- 1 p |
After |
2059 |
0 |
35 |
0 |
(a)
Simplify the ratio.
11 : 33 = 1 : 3
The allowance that Michael had at first is the same for Case 1 and Case 2.
1 p = 3 u
3 p = 9 u
The allowance that Ivan had at first is the same for Case 1 and Case 2.
9 u + 35 = 1 u + 2059
9 u - 1 u = 2059 - 35
8 u = 2024
1 u = 2024 ÷ 8 = 253
Allowance that Ivan received
= 1 u + 2059
= 253 + 2059
= $2312
(b)
Allowance that Michael received
= 3 u
= 3 x 253
= $759
Answers: (a) $2312; (b) $759