Fifty Coins
Cheryl finds a bag of coins. Can you work out how many more 5p coins than 2p coins are in the bag?
Age
11 to 14
Challenge level
Problem
Cheryl finds a bag containing 50 coins.
The value of the coins is £1.81.
If the bag only contains two-pence and five-pence coins, how many more five-pence coins are there than two-pence coins?
If you liked this problem, here is an NRICH task that challenges you to use similar mathematical ideas.
Student Solutions
Answer: $4$ more five-pence coins than two-pence coins
Forming an equation
Let the number of five-pence coins be $x$
So the number of two-pence coins is $50 - x$
Then $5x + 2(50 - x) = 181$, that is $3x = 81$, that is $x = 27$.
So there are $27$ five-pence coins and $23$ two-pence coins, so there are $4$ more five-pence coins than two-pence coins.
Starting from 25 of each coin
25$\times$2p + 25$\times$5p = 175p
Swap $n\times$2p for $n\times$5p to get 181p
175p $-n\times$2p + $n\times$5p = 181p
$\Rightarrow$ 175p + $n($5p$-$2p$)$ = 181p
$\Rightarrow$ 175p + $n\times$3p = 181p
$\Rightarrow n\times$3p = 3p
$\Rightarrow n$ = 2
After swapping 2 2ps for 2 5ps there are 4 more 5ps than 2ps