Hey everyone,
I was hoping someone who is a little better at math might be able to help me out. Not necessarily give me answers, but lead me in the right direction. Please help if you can!
1)Mary Chai invested two sums of money, the first at 10% and the second at 12%. The ratio of the amounts invested was 8:5. What was the amount of each investment if the interest on the first investment was $200 per year more than the interest on the second investment.
2)Two cars started at the same time from towns that are 615 km apart and met in 5 hours. What was the average speed of each car if one car went 15 km/hr faster than the other?
Again, I don't need the answer, just if someone could show or explain to me how to set it up, it would be greatly appreciated.
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okay....
1)
for the first one you need to set up an equation for the first too. I think it's A=P*(1+i)^n.
Now, here's how to approach it. You know that the final value at time 1 year is $200 at 10%. Therefore A = 200, i = 0.1 (remember to change the percent to a decimal), and n = 1. Plug it in, rearrange, and solve for A. Now, you know the ratio of (A for 1)/(A for 2) = 8/5, so cross multiply and solve for A2.
2)
The second one requires a series of equations. You know that D1 + D2 = 615km. You also know that T1 = T2 = 5hours. Now, you also know that V2 = V1 +15 (or you could say V1 = V2 +15) for average velocity. Now, what I would do is change the distance equation into one involving velocity and time. Velocity is equal to distance over time, or D=V/T. This transforms the equation into:
V1/T1 + V2/T2 = 615km
We're looking for V in the problem, but now we have two unknowns. To solve, use our first v equation and replace either V1 or V2. It doesn't matter which you replace, or which is faster. So when I replace with mine I get:
V1/T1 + (V1+15)/T2 = 615km
Now, we know T1=T2=5, so replace 5, solve for V1, then plug back into the average velocity equation and find V2.
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