The variable x and y represent numbers for which the statements `x-ygt300 and (y)/(x)=0.625` are true. What is the smallest integer that x can equal?

Answer

`801`

Explanation

Difficult:Hard:
Category: Heart of Algebra/ Inequalities
Strategic Advice:When you have two unknowns try to write one in terms of the other to simplify the situation.
Getting to the Answer: Solve the equation for y in terms of x:
`(y)/(x)=0.625`
`y=0.625x`
Substitute this value for y into the inequality and simplify
`x-ygt300`
`x-0.625xgt300`
`0.375xgt300`
`x=(300)/(0.375)`
`x=800`
Be careful- the inequality specifies that x must be greater than 800, so the least possible integer value of x is 801.