Barbara B. answered • 01/07/14
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Since we want the end result to be you and Jay to have an equal amount, you want to set up an equation that way. Each side of an equation is an expression. Equations are like sentences in English, and expressions are like phrases. Many times the variable is what you are looking for; in this case, the number of weeks, so let's use w as our variable.
Your expression would be: 80 + 6w, since you are saving $6 per week. Jay's expression would be -7w + 145, or 145 - 7w, which means the same thing. The fact that Jay spends his whole allowance is called extraneous information because it has nothing to do with our equation or answer, except maybe to clarify that Jay also gets an allowance.
Now set them equal to each other because you want to know how many weeks it will take for both of you to have the same amount of money.
Therefore, 80 + 6w = 145 - 7w. The number of weeks, or w, must be the same to answer the question. Since there are two w's (use an apostrophe when making a single letter plural) in our equation, the best thing to do is work your equation so there is one w first. You can either subtract 6w from both sides, or add 7w to both sides. Either way is acceptable since they follow the laws of equations. I try to tell my students to keep the variables positive if possible, to lessen the chance of making a mistake with a negative sign. So,
80 + 6w = 145 - 7w.
80 + 6w + 7w = 145 - 7w + 7w.
80 + 13w = 145
80 - 80 + 13w = 145 - 80
13w = 65
Divide both sides by 13, and you will get 5.
Don't forget to answer your problem in a complete sentence with no pronouns, if possible. For example, Jay and I will have the same amount of money after 5 weeks. Always make sure you put the unit (weeks). It is a good habit for physics, chemistry, etc.
Good luck! Moving from arithmetic to algebra can be daunting at first, but it will "click." Just persevere!
Ms. B.
