SAT Math Test 3 Question 5

In this question, we are asked to find the value of x/5 based on the expression 5/x = 15/(x+20). What we do not know from the problem is the value of x, once we have it, we can divide it by 5 and obtain our answer. To find that unknown (x), we need to solve the expression 5/x = 15/(x+20).

We can cross-multiply (fish method) that equation to obtain 15x = 5(x+20). This same expression can also be obtained if we multiply the left and right-hand sides of the starting equation by the denominators. The denominators are x and (x+20). Multiply both sides of the equation by x(x+20) will result in this:

x(x+20) [5/x = 15/(x+20)]

(5/x )x(x+20)= (15)x(x+20)/(x+20)

On the left-hand side, the x on both the numerator and the denominator will cancel out, leaving us with (5)(x+20) while on the right-hand side, the (x+20) term from the numerator and denominator will cancel out, leaving us with (15)x. We end up with the linear equality

15x = 5(x+20)

which is exactly what we obtained while cross-multiplying. What is left is to solve for x in that equation. First applying distributive properties on the right-hand side by factoring the 5 to the addends found in the parenthesis would result in

15x = 5x+100

To solve for x, the terms with the x have to be kept on one side of the equal sign while the numerical terms have to remain on the other side. In this case, we need to move the 5x on the left-hand side and switch its sign as a result. More accurately, let’s subtract 5x (or add “-5x”) on both side of the equation to eliminate the 5x from the right-hand side.

15x -5x = 5x+100 -5x

Simplifying the above expression would result in

10x = 100

10 goes into 100 ten times, therefore x = 10. Alternatively dividing both sides by 10 or multiplying both sides by one-tenth will give 10 the value of x.

Now that the value of 10 has been determined, x/5 can be computed by substituting x for its actual numerical value, 10.

10/5 = 2, making C) the option of choice.