Question 1189232
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Informally....<br>
(You can get some good mental exercise by solving a problem like this using logical reasoning and mental arithmetic)<br>
(1) Add two more 5p coins, to make the number of 5p coins exactly 3 times the number of 10p coins, and making the total value £4.50 = 450p
(2) Group the coins in groups of one 10p coin and three 5p coins, with a total value of 25p for each group
(3) The number of those groups needed to make 450p is 450/25 = 18
(4) The number of 10p coins is 18; the number of 5p coins is 3(18) = 54
(5) Take away the "extra" two 5p coins, leaving 52<br>
ANSWER: 52 5p coins<br>
CHECK: 52(5)+18(10)=260+180=440<br>
Using formal algebra....<br>
let x = # of 10p coins
then 3x-2 = # of 5p coins<br>
The total value is 440p:<br>
{{{10(x)+5(3x-2)=440}}}
{{{10x+15x-10=440}}}
{{{25x=450}}}
{{{x=450/25=18}}}<br>
ANSWER: 3x-2 = 54-2 = 52<br>