QUESTION 5
Easy
Ruby has 3 times as many two-rupee coins as she has five-rupee coins. If she has a total of ₹88, how many coins does she have of each type?
SOLUTION
1
Assume the number of five-rupee and two-rupee coins
Let the number of five-rupee coins be \(y\). Then the number of two-rupee coins is \(3y\).
2
Find the total money
Value of five-rupee coins \(= 5 × y= 5y \)
Value of two-rupee coins \(= 2 × 3y = 6y\)
Total money = \( 5y + 6y = 11y\)
Value of two-rupee coins \(= 2 × 3y = 6y\)
Total money = \( 5y + 6y = 11y\)
3
Form an equation using total money (₹88) and solve for y
\(11y = 88\)
⇒ \(y = 8\)
⇒ \(y = 8\)
4
Find the number of each type of coin
five-rupee coins \( = y = 8\)
two-rupee coins \( = 3y = 24\)
two-rupee coins \( = 3y = 24\)
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Final Answer : Ruby has 8 five-rupee coins and 24 two-rupee coins.
Concept Note
To find the number of each type of coin, let the number of one type of coin be \(x\) and express the number of the other coin using the given multiplier. Multiply by coin values to get total money equation and then solve.