2 Easy GRE questions

Question

I've been having trouble with these two questions. The first is simple interest, the second is rate. I'm sure they're easy but I can't focus on getting the solution because I'm terrible at focusing on word problems.

1) Pat invested a total of 3,000 dollars. Part of the money was invested in a money market account that paid 10% simple annual interest, and the remainder of the money was invested in a fund that paid 8% simple annual interest. If the interest earned at the end of the first year from these investments was $256, how much did Pat invest at 10% and how much at 8%?

2) Two cars started from the same point and traveled on a straight course in opposite directions for exactly 2 hours, at which time they were 208 miles apart. If one car traveled, on average, 8 miles per hour faster than the other car, what was the average speed of each car for the 2-hour trip?

Thank you

Answer 1

Hint for 1): If Pat had invested it all at $10\%$, what would it have earned? How much less is earned for each dollar invested at $8\%$ rather than $10\%$?

Answer 2

For part 2): Sometimes it helps to break out the dimensions of the problem when you form your algebraic expression. For example,

$$2 [\operatorname{hours}]\left( x\frac{[\operatorname{miles}]}{[\operatorname{hours}]} +(x+8)\frac{[\operatorname{miles}]}{[\operatorname{hours}]}\right)=208[\operatorname{miles}].$$

This way you can see that you have the right dimensions. After solving, you can of course check to see that your solution makes sense.

Answer 3

Car heading west gives $y=x*2$, car heading east gives $(208-y)=(x+8)*2$

NOTE: keep time in hours as speed is given in miles per hours.

substitute $y=2x$ in second equation to get $x$.

Do you find the term "average speed" confusing?