Video: Using Direct Variation

The cost of hiring a small car for 4 days is $170. What would the cost to hire the car for a week at the same rate be? Give your answer to two decimal places if necessary.

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Video Transcript

The cost of hiring a small car for four days is 170 dollars. What would the cost to hire the car for a week at the same rate be? Give your answer to two decimal places if necessary.

Well, the first thing to do in this kind of problem is actually get the information we need from the question. So first of all, what we’ve got is that hiring a car for four days is equal to 170 dollars. So now, in problems like this, what we want to do first is work out the cost per day. And to enable us to do that, what we’re gonna do is actually divide each side of the equation by four. And that’s because if we have the cost of four days and we want to find one day, that’s what we’ll need to do.

So therefore, we get one day is equal to- right now, I’m just gonna show you how you’d actually divide 170 dollars by four. So what we’re gonna use is short division or the bus stop method.

So we have fours into one. They don’t go. So what we’re gonna do then is carry the one. So then, we have fours into 17. And this will go four times and then we’ll carry the one. So then, we have fours into 10, which is gonna go twice, and then remainder two because two multiplied by four is eight remainder two from 10. Then, we carried that two. So then, finally, we’ve got our five because that’s 20 divided by four equals five. Okay, what we need to do now is just add a zero on the end. And we do that because we’re dealing with money. So it’s 42 dollars 50.

Okay, so we’ve now got the price per day. What’s the next stage of the problem? Well, we can see next it actually wants us to work out the cost for hiring the car for a week at the same rate. So therefore, what we need to do is actually multiply both sides of the equation by seven because obviously a week is seven days. So therefore, we’re gonna get the cost of one week is equal to.

So now, what we’ll need to do is actually multiply 42 dollars 50 by seven. What we’re actually gonna do is actually do it in two parts. First of all, we’re gonna do seven multiplied by 42 and then only seven multiplied by 0.5 or 50 cents. So first of all, we’re gonna do seven multiplied by two, which is 14. So we got four on the units column and carry the one.

And then, we’re gonna do seven multiplied by four, which is 28. So we gonna put nine in the tens column. And that’s because we had eight plus the one we carried, which gives us nine, and then finally two in the hundreds column. Okay, great, so we can say that seven multiplied by 42 is 294.

And next, we can deal with the seven multiplied by 0.5. Well, seven multiplied by 0.5 is just gonna be 3.5. And that’s because seven multiplied by five is 35. And then, when we multiply by a decimal, we need to make sure that we have the same number of digits after the decimal point as when we started. So therefore, it becomes 3.5. And also, you can think of it as half of seven and half of seven is 3.5. Okay, great, so let’s add these together and when we do that we get 297.5, remembering to add zero because we’re dealing with money.

So therefore, we can say that if the cost of hiring a small car for four days 170 dollars, then the cost to hire the car for a week at the same rate is gonna be able to 297 dollars and 50 cents.

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