SOLUTION: Solve it using a system of linear equations, showing details of how you set up your equations and the steps that you went through for the solution. You must use one of the methods

Question 970551: Solve it using a system of linear equations, showing details of how you set up your equations and the steps that you went through for the solution. You must use one of the methods in your Unit 2 Lesson (Addition/Subtraction, Substitution, Graphical Method.

A high school purchases two workbooks for every textbook, and two journals for every workbook. If the school purchases 701 total items, how many of each do they need?
Answer by josgarithmetic(39630) (Show Source): You can put this solution on YOUR website!
w, workbooks
t, textbooks
j, journals

You can also try this:
.

You have these ratios in summary:

Item sum equation would be .
w and j can be substituted from the system found above:

which is an equation in only the one variable, t.
That gives , but this makes no sense!

Purchasing 700 of these items would make better sense. The school has purchased one extra item.

------Alternative Attempt

Ratio as w:t:j format.
2:1 for workbook to textbook,
1:q:2 for workbook to journal, using q as not yet known for the textbook part.

These ratios reexpressed,
2:1:r
1:q:2
-
We want each part to be the same value, so we want to multiply one or the other ratio by some Natural Number. The ENTIRE ratio.
-
Try this for the second ratio having the q.
2(1:q:2)
2:2q:4, so we know what r must be.
Result,
2:1:4
Consistant with what was found above for j/t.

The three-part ratio shows any quantity of book items to be build of seven subparts. Two for workbook, one for textbook, four for journals.
The total items 701 is not a multiple of 7.
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