Question Video: Writing an Equation to Represent Two Quantities in a Real-World Problem Mathematics

Sophia has $10 in her bank account. Every week she will deposit $20 into the account. Write an equation that represents this situation, where 𝑇 is the total money in her account after 𝑤 weeks.

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Video Transcript

Sophia has 10 dollars in her bank account. Every week she will deposit 20 dollars into the account. Write an equation that represents this situation, where 𝑇 is the total money in her account after 𝑤 weeks.

Let’s begin this question by thinking about the money in Sophia’s bank account. At the start of this problem, Sophia has 10 dollars in her bank account. We’re told that she adds 20 dollars every week. So in the first week, she’ll have the 10 dollars plus another 20 dollars. In week two, she’ll have the 10 dollars plus two lots of 20 dollars. In week three, she’ll have 10 dollars and three lots of 20 dollars. We could also think of this week three as 10 plus three times 20 dollars. We could continue this pattern adding 20 dollars every week. This is where the variables of 𝑇 and 𝑤 will actually be quite helpful.

Somewhere along in this pattern, we will have week 𝑤. We would still have 10 dollars in the account. And although we don’t know quite how many 20 dollars we’ll have, we know that it would be equal to 𝑤 times 20. So the total in the account would be 10 plus 𝑤 times 20. We can’t just give this as our answer, however, as we’re asked to write an equation. And we’ll do this also using the letter 𝑇. As 𝑇 is the total money in the account after 𝑤 weeks, we could write this as 𝑤 times 20 or 20𝑤 plus 10. And this will be our answer for the equation. It would still have been mathematically correct to give this answer as 𝑇 equals 10 plus 20𝑤.

Before we finish this question, let’s have a closer look at the equation that we’ve written. If we were to draw a graph of this linear function, it would be a straight line graph. The value of 20 represents a constant change, and that’s because every week there were 20 dollars added to Sophia’s account. The value of 10 would be the 𝑦-intercept, this value on the graph, which show that, at week zero or the start, there were 10 dollars in the bank account. And so we can see how we’ve created a linear equation.

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