Problem Solving

Kind of confused on how to set this one up:

An instrument store gives a 10% discount to all students off the original cost of an instrument. During a back to school sale an additional 15% is taken off the discounted price. Julie, a student at the local high school, purchases a flute for $306. How much did it originally cost?


A $325
B $375
C $400
D $408
E $425

Thanks for any help y'all can give!

-Matt

This is how I would set up this question.

Set 'x' as the original cost of the instrument.

Julie first gets a 10% discount. This means she only pays 90% of the original cost.

x*.9

Then, Julie gets an additional 15% off the discounted price. She only pays 85% of the discounted price.

(x*.9)*.85

Julie pays $306, so

(x*.9)*.85 = 306

Solve for x.

That's correct. 400 is the answer.

Oh that makes so much sense now! Thank you!

I'm so rusty on math but it's starting to come back slowly.

Very appreciated,

-Matt

Hello all,

Since you have sen the theory behind sucessive discount problems, I may give you a formula that is very handy to crack these problems.

When two successive discounts are given of a% and b% then the net discount offered = a + b - (a*b)/100

Once you get the net discount percentage, one can easily claculate the price.

Cheers,
iKant

I will go with c, too

You could also just backsolve. Pick 375 and multiply it by 10%, you get a result with change, which means that there will be change in the answer, which means that it is wrong. Pick 408, same result. Try 400:

400(.10) = 40

400 - 40 = 360

360(.15) = 54

360 - 54 = 306

This all took me under 2 minutes.