Math: 5355c0ef

ID: 5355c0ef

(SAT Suite Question Bank > Find Questions > Assessment: SAT + Test: Math + Domain: Advanced Math)

Comment: This question builds off the basics of distribution and arithmetic.

Method 1: All we need to do is choose one of the values to multiply by a and match with its equivalent term on the left-hand side of the given equation. For ease, I will choose the first value, the coefficient of x^2.

0.36x^2 = a(4x^2)

36/100 = 4a

36/(4 * 100) = a

9/100 = a

The correct answer is 9/100 or .09.

Method 2: As I have explained in other questions testing equivalent expressions, you can use Desmos and split the two expressions into y = [something] and check for when the two graphs align. Create a slider for a.

The default graph is shown above. When you slide to a = 0.1, the graphs are close, but when a = 0, the blue graph covers the x-axis.

You will need to set the parameters between 0 and 1. I prefer to use a step of 0.001, just in case the answer goes into the thousandths.

When a = 0.09, the graphs overlap entirely, so the correct answer is .09.

Method 3: If the numbers 36 and 63 make you think of (multiples of) 9, then you are on the right track. You can think of what would turn the decimals into the whole numbers shown in the other expression. To get rid of the decimals, multiply by 100:

100(0.36x^2 + 0.63x + 1.17)

36x^2 + 63x + 117

Now, to turn 36 into 4 and 63 into 7, divide by 9:

4x^2 + 7x + 13

As it happens, this is the exact expression that you are told is equivalent to the other, only with a mysterious a to distribute. If we multiplied by 100 and divided by 9 to get the group to match, it stands to reason that doing the opposite—multiplying by 9 and dividing by 100—will get us to go back to the decimal. Thus, a must be 9/100, and the correct answer is 9/100 or .09.