Question

Laila tells Julius to pick a number between one and ten. “Add three to your number and multiply the sum by five,” she tells him. Next she says, “Now take that number and subtract seven from it and tell me the new number.” “Twenty-three,” Julius exclaims. What was Julius’ original number? In the next round Leila is supposed to pick a number between 1 and 10 and follow the same instructions. She gives her final result as 108. Julius immediately replies: “Hey, you cheated!” What might he mean?

Please I need this answer

Answer 1

Julius' original number is 3.

Julius said “Hey, you cheated!” because Laila did not pick a number between 1 and 10.

Explanation:

In the first round let's say Julius picked a number
`x`, when he adds 3 to it, multiplies the sum by 5, and subtracts 7 from the result, he gets

`5(x+3)-7`

and since we hear Julius exclaiming "twenty-three", this means

`5(x+3)-7 =23`

solving for
`x` we get

`x =3`.

which is Julius' original number.

In the second round when Laila picks the number and goes through the same procedure, her final result is 108, which means

`5(x+3)-7=108`

solving for
`x` we get

`x= 20`

which is Laila's number, and since it certainly is not between 1 and 10, Julius said "you cheated" by which he meant that Laila did not pick a number between 1 and 10.