Question

Matt wants to buy a television. If he pays cash, he gets a discount of 7%. If he pays with a loan he has to pay an extra 10% in interest. The difference between the two methods is $49.98. Find the cost of the television.

Answer 1

Cost of Television = $294

Explanation:

7% discount means 7/100 = 0.07 LESS

So we need to multiply by 1 - 0.07 = 0.93

Also, 10% MORE, or extra, means 10/100 = 0.10 MORE

So we need to multiply by 1 + 0.10 = 1.1

Let cost of television be "c", so we can say:

• 7% discount would mean cost to be c(0.93) = 0.93c
• 10% with interest would mean cost to be c(1.10) = 1.10c

The difference is 49.98. So we subtract lower value (0.93c) from larger value (1.10c) and equate to 49.98 and solve for c:

`1.10c-0.93c=49.98\\0.17c=49.98\\c=(49.98)/(0.17)\\c=294`

Cost of Television = $294