Algebra word problem

Question

Eric bought 3 rolls of film and 1 battery for $11. The next day he purchased 2 rolls of film and 3 batteries for $12. Find the cost of one roll of film and one battery.

 

 

 

So we are doing this for algebra but it really confused me... Please answer and explain. Please and thank you!

Answer 1

As always when doing algebra, Alice, you just assign a letter like A, B or y, z to a quantity you do not know.

 

So let us assign:

A = cost of 1 roll of film ($)

B = cost of 1 battery ($)

 

Then express the information you are given using the unknown variables:

 

Cost of 3 rolls of films and 1 battery is $11.This can be written:

3*A + B = 11

 

Cost of 2 rolls of film and 3 batteries is $12.

This can be written:

2*A + 3*B = 12

 

Now you have 2 equations with 2 unknowns, A and B.

 

You can manipulate the equations to find a way to eliminate A or B.

For example, you see the first equation has 1*B, the second equation has 3*B. So let us multiply the firs equation by 3:

 

3*A + B = 11

2*A + 3*B = 12

 

can be changed to:

9*A + 3*B = 33

2*A + 3*B = 12

 

Now I can substract the second equation from the first equation, which gives:

 

9*A - 2*A + 3*B - 3*B = 33 - 12, or

7*A = 33 - 12 = 21

 

Divide by 7 on both sides to isolate A alone:

 

7*A / 7 = 21 / 7, or

A = 21 / 7 = $3.00

 

Now that you know A, you can use any of the 2 original equations to find B.  For example, let us substitute the value of A in:  3*A + B = 11; we get

3*3 + B = 11;

 

We substract 3*3 = 9 from both sides to isolate B on the left:

3*3 - 9 + B = 11 - 9; or

B = 11 - 9 = $2.00

 

Then it is a good idea to plug in the values of A and B in your original equations again for verification. 

 

So the final answer is: a roll of film costs A = $3 and a battery costs B = $2.

 

Hope this helps!

 

  Jean-Michel