SOLUTION: For each question, define your variables, write a system of equations, and solve. Suppose you have $200 in your account and you save $10 each week. your friend has $110 in thei

Question 1092508: For each question, define your variables, write a system of equations, and solve.
Suppose you have $200 in your account and you save $10 each week. your friend has $110 in their account and starts saving $15 each week. when will your account balances be the same?
Joey has $5.75 made up of all dimes and quarters. if joey has 38 coins, how many of each coin does he have?
Thank you!
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

You need to know how to do this yourself. I will just get you started....

First problem...

variables: There is only one variable here -- the number of weeks you and your friend add to your accounts to make the amounts the same.

system of equations: There is only one equation. It says the amount in your account after some number weeks (the original 200, plus 10 more each week) is equal to the amount in your friend's account after that same number of weeks (the original 110, plus 15 more each week).

solving: That is what you need to be able to do....

By the way, the above description is of a formal algebraic solution, which you seem to be asking for. A faster informal solution to the problem says that your friend is initially 90 behind you and is catching up by 5 each week; the number of weeks it will take him to catch up is 90/5 = 18.

Second problem...

variables: while you could solve this using a single variable, the way the problem is presented makes the use of two variables -- the number of quarters and the number of dimes -- the usual choice.

system of equations: You have two pieces of information with which to make equations involving your variables. (1) the total number of coins is 38; and (2) the total value of the coins (25 cents for each quarter, plus 10 cents for each dime), is $5.75 (i.e., 575 cents).

solving: again, that is for you to do; otherwise you will learn nothing from this.
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