Can I ask two more questions?

Question

Mike invested $6000 for one year. He invested part of it a 9% and the rest at 11%. At the end of the year he earned $624 in interest. How much did he invest at each rate?

Car rental agency A will rent a compact car for $35 per day and an additional charge of $0.24 per mile. Car rental agency B will charge only $0.16 per mile but charges $41 per day. If Adam wanted to rent a car for three days, bow many miles would Adam have to drive to make car rental agency B a better bargain?

Dutchmaster, you are right I need to learn the formulas myself, however I never had any good math teachers. I think once I entered high school that changed, but it wasn't because I wasn't willing to learn. The teachers just were that interested I guess.

Answer 1

It is really nice of these people to do your homework for you. I hope you go over it and learn how to do it and don't just copy the answers.

Answer 2

First Question

Let x = amount invested at 9%
so, 6000 - x is amount invested at 11%

Interest earned is equal to principal x rate x time
... in this case, the principal is x, rate is 9% expressed as 0.09, and time 1 year

... PLUS

... principal (6000 - x), rate 11% expressed as 0.11, and time 1 year.

... EQUALS

... $624 (total interest earned)


This gives the formula as follows:

0.09x + 0.11(6000 - x) = 624 which is solved as follows:

0.09x + 660 - 0.11x = 624 (removing parenthesis using distributive property)

-0.02x + 660 = 624 (simplify left side of equation)

-0.02x = -36 (subtract 660 from both sides)

x = 1800 (divide both sides by -0.02)

Therefore, $1800 is invested at 9% and
6000 - 1800 or $4200 is invested at 11%.
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To check this:

$1800 at 9% is 1800 times 0.09 or $162 from this investment and ...
$4200 at 11% is 4200 times 0.11 or $462 from this investment ... for a total of $624 interest received.

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SECOND QUESTION

Let x = miles driven
Agency A charges 3($35) + 0.25x
Agency B charges 3($41) + 0.16x

Driving a few miles, Agency A would be best. To find the number of miles that the two agencies would charge the same, set the two charges equal to each other for the equation as follows and solve:

3($35) + 0.25x = 3($41) + 0.16x
105 + 0.25x = 123 + 0.16x
..... subtract 0.16x from both sides to get
105 + 0.09x = 123
..... subtract 105 from both sides to get
0.09 = 18
..... divide both sides by 0.09 to get

x = 200

Therefore, the agencies charge the same amount for traveling 200 miles.

Anything less than 200 miles, Agency A would be the better bargain. Anything over 200 miles, Agency B would be a better bargain.
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To check this,
201 miles would cost as follows:

Agency A ----- 105 + 0.25(201) = 105 + 50.25 = $155.25
Agency B ----- 123 + 0.16(201) = 123 + 32.16 = $155.16

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FINAL ANSWERS:

Question 1
.... $1800 at 9% and $4200 at 11%

Question 2
.... 201 miles for agency B to be the better bargain

Answer 3

105+.24x=123+.16x
x=22.5
Car agency B to be a better bargain would be 23 miles.

Answer 4

would love to help you do your hiomework but you need to learn the formulas yourself .