The sparky valley barbershop quartet made appearances in Quakertown and Doleystown. The hotel charge before taxes in Doleystown was $500 higher than Quakertown. The tax in Quakertown is 3% and Doleystown is 6%. The total hotel tax from the two places is $480. How much did each hotel charge the Quartet before taxes?

In this question, we have a musical band that visited two different towns which hotel charge different amounts at different tax rate. We are now given the total amount in taxes and now asked to calculate what is charged in each of the towns.

Let’s proceed!

Since we do not know the amount charged in each of the towns, let the amount charged at the hotel at Quakertown be $x and the amount charged at the hotel at Doleytown be $y.

Doley charged $500 more then what is charged at Quaker.

Mathematically;

y = 500 + x •••••••••••••••(I)

Let’s now work with the taxes;

Tax rate at Doley is 6% or say 0.06; the amount of tax paid at Doley is thus 0.06y

Tax rate at Quaker is 3% or say 0.03; the amount of tax paid at Quaker is thus 0.03x

Mathematically;

0.06y + 0.03x= 480 •••••••••(ii)

We can substitute i into ii

0.06(500 + x ) + 0.03x = 480

30+ 0.06x + 0.03x = 480

30 + 0.09x = 480

0.09x = 480 - 30

0.09x = 450

x = 450/0.09

x = $5,000

y = 500 + x

y = 500 + $5000 = $5,500