Question

Please help!!! If you could show a step by step it would be amazing thank you!!

1. A group of friends decided to rent a house in Aspen, Co for a week of skiing. They each had to chip in $70 for lodging. If they had been able to convince three more people to go, the cost per person would have been reduced by $14. What was the cost of lodging for the week.

2. Maria took three college algebra exams and had an average score of 84. Her second exam was eight points better than her first and her third exam was eleven points better than her second exam. Find the three exam scores.

3. A total of $12,000 was invested, part at 6% and the remainder at 8%. Find how much was invested at each rate, if the total yearly interest earned was $820.

4. Xurry invests a certain amount of money at 7% interest and $1500 less than that amount at 4.5%. His yearly interest is $392.50, find how much he invested at each rate.

Answer 1

2. exam 1 - 84, exam 2 - 92, exam 3- 103

average: 93

Explanation:

exam 2 was 8 points higher means 84+8=92

exam 3 was 11 points better than exam 2 which means 92+11=103

average was a just in case. just add all three numbers and divide by three since thats how many exams there were and that is the average score for the three exams

Answer 2

1. The total cost of the lodging would be divided by the amount paid by each person is written as r/70

If 3 more people went the cost per person would be $14 less

The new total cost would be r/(70-14) = r/56

The equation becomes r/70 + 3 = r/56

Find the least common denominator and multiply each term by that.

The LCM of 70 and 56 is 280

Now you have 280 * r/70 + 3*280 = 280 * r/56

Simplify:

4r + 840 = 5r

Subtract 4r from each side:

r = 840

The cost of lodging is $840

2. 3 exams averaged 84, so the total points would be the number of exams times the average score: 3 x 84 = 252 total points.

Let the 1st exam be X, then the second exam is x+8 ( 8 points better).

The third exam is x + 8 + 11 = x+19 ( 11 points better than the second exam.

Now you have x + x+8 + x +19 = 252

Simplify:

3x + 27 = 252

Subtract 27 from both sides:

3x = 225

Divide both sides by 3:

x = 225/3 = 75

First exam = x = 75

2nd exam = x +8 = 75 + 8 = 83

3rd exam = x +19 = 75 + 19 = 94

3. Let the amount invested at 6% = X and the amount at 8% = y

We know X +y = 12,000 and 0.06x + 0.08y = 820

Multiply the second equation by 100 to remove decimals:

Now you have x +y = 12,000 and 6x +8y = 82000

Rewrite the first equation as X = 12000 -y

Replace x in the second equation:

6(12000-y) + 8y = 82000

Simplify:

72000 - 6y + 8y = 82000

72000 + 2y = 82000

Subtract 72000 from both sides:

2y = 10000

Divide both sides by 2:

y = 5,000

$5000 was invested at 8% and 7,000 was invested at 6%

4. Let the amount invested at 7% = x, then the amount invested at 4.5% would be (x - 1500). Write the equation:

0.07x + 0.045(x-1500) = 392.50

Simplify:

0.07x + 0.045x - 67.50 = 392.50

0.115x - 67.50 = 392.50

Add 67.50 to both sides:

0.115x = 460

Divide both sides by 0.115

x = 460/0.115 = 4000

They invested $4000 at 7% and (4000-1500) $2500 at 4.5%