Problem Solving

Hi there,

I would like to know the simplest process to resolve this PS. Explanation is requested.

Connie paid a sales tax of 8 percent on her purchase. If the sales tax had been only 5 percent, she would have paid $12 less in sales tax on her purchase. What was the total amount Connie paid for her purchase
including sales tax?

a) 368
b) 380
c) 400
d) 420
e) 432

If the sales tax had been only 5 percent, she would have paid $12 less in sales tax on her purchase

so 3 percent is 12 dollars
3x/100 =12
x=400
and the 8 dollars tax ..that is 32 dollrs

so she paid 432 dollars in total
answer E

Connie's purchase= $x

.05(x)=.08(x)-12

-.03(x)=-12

x=400

400*1.08=432

E

Xbond wrote:Hi there,

I would like to know the simplest process to resolve this PS. Explanation is requested.

Connie paid a sales tax of 8 percent on her purchase. If the sales tax had been only 5 percent, she would have paid $12 less in sales tax on her purchase. What was the total amount Connie paid for her purchase
including sales tax?

a) 368
b) 380
c) 400
d) 420
e) 432

p=purchase price
x=amount she paid plus sales tax

problem gives you two equations which you can solve by substitution or systems of equation.

x=1.08p and (x-12)=1.05p

x-1.05p=12
1.08p-1.05p=12
108p-105p=1200
3p=1200
p=400

400(1.08)=432 -->Answer E