Chapter 2: Introduction to Linear Polynomials

Exercise

Question

Question: 5

9 / 11

Ruby has 3 times as many two-rupee coins as she has five-rupee coins. If she has a total ₹88, how many coins does she have of each type?

Answer

1
Let the number of five-rupee coins be x. Use the given relationship to express the number of two-rupee coins.
Five-rupee coins = $x$
Two-rupee coins = $3x$
2
Find the total value of all the coins and use the given total of ₹88.
\text{$(5 × x) + (2 × 3x) = 88$ $\quad$ ${color:#625b5f}[Total value of five-rupee and two-rupee coins = ₹88]{/color}$}
⇒
$5x + 6x = 88$
⇒
$11x = 88$
⇒
\text{ $x = \dfrac{88}{11}$}
⇒
\text{ $x = 8$ $\quad$ ${color:#625b5f}[Number of five-rupee coins]{/color}$}
3
Find the number of two-rupee coins.
\text{$3x = 3 × {color:#2E2EFF}8{/color} = 24$ $\quad$ ${color:#625b5f}[Number of two-rupee coins]{/color}$}
4
Write the number of coins of each type.
Answer: Ruby has 24 two-rupee coins and 8 five-rupee coins.
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