Answer:
The hotel at Qakertown charged $5000 before tax while the hotel at Doleystown charged $5,500 before tax
Step-by-step explanation:
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
