1. A student took out two loans totaling $6000 to help pay ...

1. A student took out two loans totaling $6000 to help pay for college expenses. One loan was at 7% simple interest and the other was at 5%. After one year, the student owed $340 in interest. Find the amount if the loan at 5%.

Please show ALL work on this question. Let: x = amount of the first loan y = amount of the second loan x+y = 6000 (1) 0.07x+0.05y = 340 (2) Then: doing 100(2) x+y=6000 (3) 7x+5y = 34000 (4) Changing (4) by 7(3)-(4) x+y=6000 (5) 2y = 8000 (6) From (6) we have: y = 4000 From (5) x+4000 = 6000 then x = 2000 Answer: amount of the loan at 5% is $2000

2. The sum of two numbers is 72, and twice their difference is 24. What is the smaller of the two numbers?

Please show ALL work on this question.

Let x and y those numbers

x+y=72 (1) x-y=24 (2)

Adding the equations:

2x = 96 then x=48, using (1) 48+y=72 then y =24

Numbers are: 48 and 24

Answer: the smallest number is 24

3. Translate the problem situation to a system of equations. Do not attempt to solve.

Two angles are supplementary. One angle is 30? more than three times the other angle. Find the measure of the angles. (Let x and y represent the angles.)

Answer:

x+y = 180 x = 3y+30

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