Algebra word problem

Question

You order two servings of pancakes and a fruit cup. The cost of the fruit cup is $1.50. You leave a 15% tip. Your total bill is $11.50. How much does one serving of pancakes cost?

Answer 1

Let us denote the price of a serving of pancakes as A and the price of a fruit cup as B ; the total cost of your order without tip as C and the total you paid as D.

 

Then you can write this situation as

 

2A +B= C  (Equation I)  meaning that is 2 servings of pancakes (A)  and one cup of  fruit (B) will cost you C

 

but you are going to leave a 15% tip,  that is a 15 % of your total cost C that means that your tip equals 0.15*C and you need to add that to our previous equation:

 

2A + B + 0.15C = D    substituting C by 2A +B 

 

2A + B + 0.15(2A +B) = D (Equation II)

 

You can now substitute B by the known price of the fruit cup which is $1.50, D by the total you paid ( $11.50 )

 

after substitution you have that:

 

11.50 = 2A + 1.50 + 0.15( 2A + 1.50)              (Equation III)

 

you need now to distribute 0.15( 2A + 1.50) by multiplying 0.15 by both terms between parenthesis

 

0.15( 2A + 1.50) =  0.15*2A + 0.15*1.50 = 0.3A +0.225

 

11.50 = 2A + 1.50 +0.3A +0.225            (Equation IV)

 

Combining like terms you have

 

2A+0.3A= 2.3A  

 

1.50+0.225 = 1.725

 

your equation now is:

 

11.50 = 2.3A + 1.725      (Equation V )

 

Solving the equation V for A:

 

11.50 - 1.725 = 2.3A

 

9.775 = 2.3A

 

A = 9.775 / 2.3

 

A = 4.25

 

To check our calculations we are going to substitute A,B and D in our Equation III:

 

11.50 = 2A + 1.50 + 0.15( 2A + 1.50)

 

11.50 = 2*4.25 +1.50 + 0.15( 2*4.25 + 1.50)

 

11.50= 8.50 +1.50 + 0.15( 8.50 + 1.50 )

 

11.50= 8.50 +1.50 + 0.15(10 )

 

11.50= 8.50 +1.50 + 1.50

 

11.50 = 11.50   

 

 

If you want to know how much your tip was you can now find C and then calculate 15% of C:

2A + B= C (Equation I)

 

C = 2*4.25 + 1.50 = 8.50 + 1.50 = 10

 

Tip= 0.15C = 0.15*10 = 1.50

 

I hope this was useful for you.

 

 

 

 

 

 

2A +B= C  (Equation I)
2A + B + 0.15C = D