To approach word problems, you could follow the steps:
1. Read and understand the problem, identify the unknown to be calculated.
2. Designate an algebraic symbol to stand for the unknown, or one of the unknowns.
3. Reread the question, interpret the information given in terms of the unknowns.
In the case where a simple relationship relates two or more unknowns, express the other unknowns in terms of the one that has an algebraic symbol.
4. Formulate a mathematical equation in terms of the algebraic symbol.
5. Solve for the unknown, if possible. Evaluate the other unknowns expressed in terms of the algebraic symbol.
6. Interpret the results in words.
7. Check the calculated results.
The example given will illustrate the procedure.
1. Unknowns to be calculated: quantities sold by DQ and Sonic.
2. Since a simple relationship relates the two ("DQ sells 6 times as many orders of french fries as sonic everyday."), we will designate only one variable,
S = initial daily sales by Sonic
3. Reread the question:
"DQ sells 6 times as many orders of french fries as sonic everyday."
6S = daily sales by DQ
"If both sold 60 more orders DQ would only sell 3 times as many fries."
Noting that we denote initial sales of DQ by 6S:
3 times (S+60 more sales) = (6S + 60 more sales)
4. Formulate an equation
From (3) above, we conclude that the equation is:
3(S + 60) = (6S + 60)
5. Solve the equation:
Expand the terms:
3S + 3*60 = 6S + 60
3S + 180 = 6S + 60
Collect terms containing S on the left-hand side:
3S - 6S = 60 - 180
-3S = -120
Solve for S:
S = -120 / (-3) = 40
6. Interpret the results:
S=40= initial sales by Sonic.
6S = 240 = initial sales by DQ
S+60 = 100 = increase sales by sonic
6S+60 = 300 = increased sales by DQ
240/40 = 6 times (OK)
(240+60)/(40+60) = 300/100 = 3 times (OK)
Petie--I gave you two equations yesterday and told you to solve the two simultaneous equations. Matmate gave you some very good directions as a way to approach word problems. Perhaps you need to review the mechanics of how to solve simultaneous equations, also.
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