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Algebra Level 2

My son has bought himself a new car at $34300 from a shop after three successive discount of 30 % 30 \% . When I went to the shop, they did not offer any more discounts, and I still bought the same car.

How much did my family (both my son and I) spend on cars?

Image credit: Wikipedia NRMA Motoring and Services


The answer is 134300.

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3 solutions

Let x x be the original price. The first discount is x 0.3 x = 0.7 x x-0.3x=0.7x . The second discount is 0.7 x 0.3 ( 0.7 x ) = 0.49 x 0.7x-0.3(0.7x)=0.49x . The third discount is 0.49 x 0.3 ( 0.49 x ) = 0.343 x 0.49x-0.3(0.49x)=0.343x .

Then

0.343 x = 24300 0.343x=24300

x = 100000 x=100000

t o t a l a m o u n t = 100000 + 34300 = total~amount=100000+34300= 134300 \color{#D61F06}\boxed{134300}

Tushar Malik
Mar 13, 2015

Let the actual cost of the car before discount be x x .

After the 1st discount the cost is x x - 30 100 x \frac{30}{100}x = = 70 100 x \frac{70}{100}x .

Similarly after the 2nd discount the cost is 70 100 x \frac{70}{100}x - 30 100 x × 70 100 x \frac{30}{100}x \times \frac{70}{100}x = = 49 100 x \frac{49}{100}x .

Same way is followed and after the 3rd discount the cost will be 343 1000 x \frac{343}{1000}x .( After this no further discount is implemented.)

Now, we get 343 1000 x \frac{343}{1000}x = = 34300 34300 .

Thus, the actual cost of the car was $ 100000 \$100000 .

Therefore, the total money spent on the cars is 34300 + 100000 = $ 134300 34300 + 100000 = \$134300 ( It is because the father bought the car without any discount.)

Jacob Jones
Apr 2, 2015

If a 30% discount has been applied, we can assume that our price is 0.7 of the original. therefore we can divide by 7 and multiply by ten, We do this three times for the three successive discounts of 30% which gives us a price of $100000. We add these together to get $134300

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