Oracle SAT Math Problem Explanation!
Explanation and Tips!
To solve this problem quickly, pick real dimensions for the rectangle. Let’s say the rectangle is 10 by 10. That makes the original area of the rectangle 100.
According to the problem if we increase the length by 10% and decrease the width by s percent, the new area will be decreased by 12%. This means the new area would be 88.
Our length of 10 is increased by 10%, so it will now equal 11.
So really, the question is asking what dimension, when multiplied by 11, is equal to 88? Or even better, 88 divided by 11 is what?
Keep in mind that for the width, we need to decrease 10 by s percent. So for answer choice A, 10 decreased by 12% would be 8.8. For answer choice B, 10 decreased by 15% would be 8.5.
Test each answer choice until you find the dimension s that gives you an area of 88. The answer is C! A length of 11 and width of 8 will give you a total area of 88!
Two quick tips from this problem:
To decrease 100 by 12%, you can either A) find 12% of 100 and then subtract that from 100 or B) find 88% of 100. B) saves you time and a calculation!
Picking real values to work with will help the accuracy of your work. The algebraic equation for solving this question looks like this:
.88(xy) = (1.1x (1-.s)y)
...and coming up with this much less solving it is time consuming and very prone to error. Instead, plug in values!