Roger wants to buy a smartphone that cost three hundred and four dollars. If he saves thirty-eight dollars each week, determine in how many weeks he will be able to buy his smartphone. Our question is asking us how many weeks it will take for him to save enough money to buy a smartphone.
We know that Roger saves thirty-eight dollars each week. We also know that the phone costs three hundred and four dollars. We start by saying that Rogers saves thirty-eight dollars per week. That per week means we can say thirty-eight times 𝑤 for weeks. So if we multiply thirty-eight times the number of weeks he’s saving, we will find out how much money Roger has saved so far. And we want the amount that he has saved to equal the cost of the phone, three hundred and four dollars. We want thirty-eight dollars times the number of weeks he saved to equal three hundred and four dollars.
But now what? Now when we have this equation, what can we do? We could try to add thirty-eight plus thirty-eight plus thirty-eight plus thirty-eight over and over again until we got to three hundred and four. But that’s not a very effective way to answer this question. We’re gonna answer the question by dividing both sides of our equation by thirty-eight.
So let’s note that if we divide thirty-eight 𝑤 by thirty-eight, the solution would be one 𝑤 or simply 𝑤. On our left-side of the equation, we’re left with only 𝑤. When we divide three hundred and four by thirty-eight, the solution is eight.
The number of weeks it would take Roger to save up three hundred and four dollars is eight, eight weeks. If you wanted to check and make sure we did everything correctly, you could plug that eight back into our equation, thirty-eight times eight, and ask does that equal three hundred and four. And it does. Roger needs to save for eight weeks.