john paid $35 for 2 algebra and 3 geometry books. he paid $36 for 3 algebra and 2 geometry books. what is the cost of each book?

Question

i really need help doing this I don't get this at all. please help!! thank you

Answer 1

Let a be the cost for an algebra book. Let g be the cost of a geometry book.

 

2a + 3g = 35 and

3a + 2g =36

 

Multiply first math sentence by -3 and second sentence by 2. Why? To cancel the a out and have only one variable left over. Then solve for g. 

 

-6a - 9g = 105

6a + 4g = 72

                      

-5g = -33 Therefore

g or the cost of a geometry book is $6.60. Now substitute 6.6 for g in either sentence one or two to get:

I choose sentence one. 

 

2a + 3 (6.6) =35

2a + 19.8 =35

2a = 35 -19.8

2a = 15.2

2        2

a = 7.6

since a refers to cost convert 7.6 to dollars and cents.

 

 

a or the cost of an algebra book is $7.60

 

 

 

 

Answer 2

Let A = cost of one Algebra book & let G = cost of one Geometry book.  The two given facts are, in equation form,

2A+3G = 35

3A+2G=36

Then you solve these equations, by using any method that has been taught in your algebra class.  Substitution might be a good one, i.e. solve the first equation for A, then plug that expression into the second equation, solving for B. Then back to the first equation, knowing B, and thus finding A.  Check the answers in both equations.

 

Good luck!