Question

1st Question: Dominic pays 7% interest on his $18,000 college loan and 12% interest on his $14,000 car loan. What average interest rate does he pay on the total $32,000 he owes? (Round your answer to the nearest tenth of a percent.)

2nd Question: The ice rink sold 95 tickets for the afternoon skating session, for a total of $828. General admission tickets cost $10 each and youth tickets cost $8 each. How many general admission tickets and how many youth tickets were sold?

Answer 1

1) The average interest rate he will pay on the total $32,000 he owes 9.2%

2) General tickets is 34 and youth tickets is 61

Explanation:

1st Question:

Total money owed = $32,000

Interest paid on $18,000 is 7% ==> 18,000 x 0.07 = 1,260

Interest paid on $14,000 is 12% ==> 14,000 x 0.12 = 1,680

To find Average interest rate:

Let 'X' be interest paid on $32,000 ==> 32,000*X

Total interest paid = Sum of all interests

32,000*X = 1,260 + 1,680

32,000*X = 2,940

X = 0.0919

∴ X = 9.2%

2nd Question

Value of 95 tickets is $828

Youth ticket cost is $8

General admission cost is $10

Let 'Y' be Number of youth tickets sold, Number of general admission tickets is 95 - Y since the total number of ticket is 95.

Value of 95 - Y general admission tickets is (95 - Y)10

Value of Y youth tickets is 8Y

Total value is $828

(95-Y)10 + 8Y = 828

950 - 10Y + 8Y = 828

122 = 2Y

Y = 61

Recall that, number of general admission tickets is 95 - Y ==> 95 - 61 ==> 34