Final answer:
The number is -40.
Step-by-step explanation:
To solve this problem, let's break it down step by step:
Let's assume the number is x.
The sum of a number and eight is x + 8.
A quarter of the sum of a number and eight is (1/4)(x + 8).
Double the number is 2x.
One fifth of double the number plus seven is (1/5)(2x) + 7.
The difference of a quarter of the sum of a number and eight and one fifth of double the number plus seven is [(1/4)(x + 8)] - [(1/5)(2x) + 7].
We know that this difference equals 10, so we can set up the equation: [(1/4)(x + 8)] - [(1/5)(2x) + 7] = 10.
Simplify the equation: (1/4)(x + 8) - (2/5)x - 14 = 10.
To get rid of the fractions, multiply the entire equation by the least common denominator, which is 20: 5(x + 8) - 8(2x) - 280 = 200.
Simplify the equation: 5x + 40 - 16x - 280 = 200.
Combine like terms: -11x - 240 = 200.
Add 240 to both sides: -11x = 440.
Divide both sides by -11: x = -40.
The number is -40.