SOLUTION: An electronics store offers separate discount coupons of 5%, 10%, and 15%. Bill uses one of each coupon to buy a computer with sticker price $1000. When Bill gets his receipt, a

Question 1209199: An electronics store offers separate discount coupons of 5%, 10%, and 15%.
Bill uses one of each coupon to buy a computer with sticker price $1000.
When Bill gets his receipt, a dark smudge covers up the sales tax percentage, but he can see the final total at the very bottom of the receipt is $773.99
(a) What is the sales tax percentage? Round to the nearest tenth of a percent.
(b) If there wasn't any sales tax, how much would Bill spend? Round to the nearest penny.
Found 2 solutions by math_tutor2020, ikleyn:
Answer by math_tutor2020(3817) (Show Source): You can put this solution on YOUR website!

Answers:
(a) 6.5% sales tax
(b) $726.75

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Explanation for Part (a)

The discount multipliers are of the form (1-r) where 0 < r < 1
An example is r = 0.05 represents a 5% discount.
Let x be the unknown tax rate in decimal form where 0 < x < 1.
(1+x) is the sales tax multiplier.

Chaining the discounts and sales tax multipliers together will yield:
(1-0.05)*(1-0.10)*(1-0.15)*(1+x) = 0.72675(1+x)
This represents the proportion of the original price the customer pays.
startPrice*thatProportion = finalPrice
1000*0.72675(1+x) = 773.99

I'll let the student handle the scratch work in terms of solving that equation.
You should get this approximate solution: x = 0.0650017
That converts to 6.50017% and rounds to 6.5% sales tax (when rounding to the nearest tenth of a percent).

Check:
1000*(1-0.05)*(1-0.10)*(1-0.15)*(1+0.065) = 773.98875 which rounds to 773.99

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Explanation for Part (b)

The quick calculation would be
1000*(1-0.05)*(1-0.10)*(1-0.15) = 726.75
Since we can multiply in any order, the order of the discounts doesn't matter.

Answer by ikleyn(52813) (Show Source): You can put this solution on YOUR website!
.
An electronics store offers separate discount coupons of 5%, 10%, and 15%.
Bill uses one of each coupon to buy a computer with sticker price $1000.
When Bill gets his receipt, a dark smudge covers up the sales tax percentage,
but he can see the final total at the very bottom of the receipt is $773.99
(a) What is the sales tax percentage? Round to the nearest tenth of a percent.
(b) If there wasn't any sales tax, how much would Bill spend? Round to the nearest penny.
~~~~~~~~~~~~~~~~~~~~~~~~

If I understand correctly, Bill uses 3 coupons of 5%, 10%, and 15%. If so, then his buying price before the tax is (1-0.05)*(1-0.1)*(1-0.15)*1000 = 0.95*0.9*0.85*1000 = 726.75 dollars (the precise value). Hence, the tax is 773.99 - 726.75 = 47.24 dollars. It means that the tax rate is = 0.065002, or 6.5002%. Round it as requested to get the answer to (a) as 6.5%. The answer to (b) is $726.75, which we got above.

Solved.

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