Answer:
Step-by-step explanation:
Let <u>M</u> and <u>S</u> be the numbers of Math and Science books, respectively. Let <u>T</u> 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: <u>7S = T - 6</u> [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: <u>9M = T + 8</u> But since we know he is buying the same number as science, we can also write this as <u>9S = T + 8 </u>[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 <u>if</u> 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.
