Question

Peter has $20 and Paul has $212. when they each given $x,Paul has 5 times as much as Peter. Write down an equation in x and solve it.?

Answer 1

Explanation:

Peter had 20 dollars and Paul has 212 dollars initially. Each of them were given $x and now Peter has 5 times as much as peter.

Final amount both of them had:

• Peter = $20 + x
• Paul = $212 + x

5 times the money Peter had (the final amount) is equals to that of Paul's. Writing down the equation,

`\rm{5(Peter's \: money) = Paul's \: money }`

`\implies \: 5(20 + x) = 212 + x`

Now solving the equation, starting with opening the parentheses,

`\implies{100 + 5x = 212 + x}`

Subtracting 5x from both sides,

`\implies {100 + 5x - 5x = 212 + x - 5x}`

`\implies{100 = 212 - 4x}`

Now shifting 212 to the other side for isolating 4x,

`\implies{4x = 112}`

Dividing 4 both sides,

`\implies{x = 28}`

Therefore, value of x is $28, Peter and Paul were given an amount of 28 dollars each and their amount became 48 dollars and 240 dollars respectively. (240 = 5*48)