Question

Peggy is thinking of a number such that when twice the number is added to three times one more than the number she gets the same result as when she multiplies four times one less than the number. What number is Peggy thinking of?

Answer 1

-7

Explanation:

Lets assume the number Peggy is thinking of be "x".

Now as given, when twice the number is added to three times one more than the number. We can write it as

∴
`2x+3(x+1)`--- Equation 1

Again, it is given that Peggy gets the same result as when she multiplies four times one less than the number.

∴
`4(x-1)`-- equation 2

Next, we can equate both the equation 1 and 2 as it is given that result is same.

`2x+3(x+1)= 4(x-1)`

Let´s distribute 3 into
`(x+1)` and 4 into
`(x-1)`

⇒
`2x+3x+3=4x-4`

⇒
`5x+3=4x-4`

Subtract both side by 4x and 3

∴
`x=-7`

∴ Peggy was thinking of -7