Question

A math book costs $9 and a science book costs $7. If Steve spends all his money in the science books, he still has $6 left. However, if he buys the same number of math books, he needs another $8 more.
A. How much books is Steve buying?
B. How much money does he have?

Answer 1

A. 7 books each
B. he has $55

Answer 2

Answer:

Step-by-step explanation:

Let M and S be the numbers of Math and Science books, respectively.  Let T be Steve's Total money he has to play with.

We are told that if Steve splurges (as he should) on nothing but science books. he has $6 left.

We can write this as:  7S = T - 6  [The number of science books, S, times $7 each, leaves Steve with only $6 (T - 6).]

We also find that if he buys the same number of math books, he'll need $8 more.  Zounds.  But we can write this as:  9M = T + 8  But since we know he is buying the same number as science, we can also write this as 9S = T + 8    [The same number as he bought for science, S, times $9, Steve needs another $8].

We have two equations and two unknows (S and T), so lets see if we can solve for these variables.

7S = T - 6

9S = T + 8

Let's rearrange the first:  T = 7S + 6

Now use that  vale of T in the second equation:  

9S = T + 8

9S = (7S + 6) + 8

2S = 14

S = 7  That's 7 Science books.  It's also the value of M, 7 math books, since the problem states if he bought the same number as science books.

Now use S = 7 to find T, the total money Steve has [after coffee and doughnuts].

7S = T - 6

7*7 = T - 6

T = 49 + 6

T = $55

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Let's see if $55 works for both the science and math book options:

1.  7 Science books:  $7/(S book)*(7 books) = $49  [He has $6 left]

2.  7 Math books:  $9/(M book)*(7 books) = $63  [He needs $8 more]

These results match the problem statements.

Steve has $55 (T).  He can buy either  7 science books or 6 math books:

Math:  6*($9) = $54  with $1 left, or

Science:  7*($7) = $49 with $6 left.

I suggest 6 Science books ($42) and 1 Math book ($9) for a total of $51, and still have $3 for coffee.  We aren't told if these books are all different from one another.  If they aren't, then Steve needs to ponder why he needs duplicated books.