Algebra 1, equation problem

Question

Mark is saving money to buy a game system. He has $100 in his bank already and plans to save $25 per month. Write an equation that represents how much money Mark will save. Let x represent the number of months and y represent the total amount in his bank account. I have no idea how to write this equation out, please help.

Answer 1

If we consider the equation for linear growth,

y = m*x + b

which you should be familiar with, we can think about how this problem applies.

We're told that Mark has already got $100 dollars in his bank account, or in other terms, there is a constant $100 dollars in his account. That value isn't changing. If we take a look at the form for linear growth, we can reason that b = 100, as there are no coefficients or exponents on b that would change it's value. This should make sense because we know that his $100 dollars starting savings is a constant, it won't change.

We're also told that Mark plans on saving $25 dollars a month. We can determine that this value is a rate because we have a value over a unit in time, dollars per month in this case. Looking back on our form for linear growth, we know that $25/month won't be x or y, and we know that we want x to represent the number of months Mark has been saving for. By elimination, we know that m = 25, but take a moment and think about why this makes sense. We have a rate multiplied by a time, which has to equal a constant since we can't say that Marks bank account has "$25 dollars a month and $100 in savings." If you travel 60 miles an hour for an hour, how far have you gone? 60 miles.

Put it all together and we can see that the equation for how much money Mark has in his account is

y = 25*x + 100

these problems can be tricky, but always think about what numbers and units make sense when being added, multiplied, or divided by one another.

Answer 2

Hello!

If y is the total in his bank account, then our equation has to be 25 times how many months he saves plus the $100 he already has. The equation will look like this:

y=100+25x