Riordan and Tim were given some allowances each. If Riordan spent $17 each day and Tim spent $51 each day, Riordan would still have $1794 left when Tim spent all his allowance. If Riordan spent $51 each day and Tim spent $17 each day, Riordan would still have $26 left when Tim spent all his allowance.
- How much allowance did Riordan receive?
- How much allowance did Tim receive?
|
Case 1 |
Case 2 |
|
Riordan |
Tim |
Riordan |
Tim |
Before |
1 u + 1794 |
3 u |
3 p + 26 |
1 p |
Change |
- 1 u |
- 3 u |
- 3 p |
- 1 p |
After |
1794 |
0 |
26 |
0 |
(a)
Simplify the ratio.
17 : 51 = 1 : 3
The allowance that Tim had at first is the same for Case 1 and Case 2.
1 p = 3 u
3 p = 9 u
The allowance that Riordan had at first is the same for Case 1 and Case 2.
9 u + 26 = 1 u + 1794
9 u - 1 u = 1794 - 26
8 u = 1768
1 u = 1768 ÷ 8 = 221
Allowance that Riordan received
= 1 u + 1794
= 221 + 1794
= $2015
(b)
Allowance that Tim received
= 3 u
= 3 x 221
= $663
Answers: (a) $2015; (b) $663