An office supply store charges 344 dollars for each pair of office chairs. A recent discount by the store offered five chairs for 770 dollars. Determine how much Mr Thomas would save per chair if he purchased this offer.
This question is all about some office chairs that are being sold by an office supply store. And there are two prices that we’re told about. Firstly, we’re told that the store charges 344 dollars for each pair of office chairs. In other words, in the shop, 344 dollars will buy you two chairs. The second price we’re told about is a discount. And here, the store was offering five chairs for 770 dollars.
The question asked us to work out how much Mr Thomas would save if he purchased the offer — in other words, if he paid the discount price. We might think he wouldn’t save anything. 770 dollars is a lot more than 344 dollars. Surely, he’s paying more money. There’re two little words in our final sentence that we need to take notice of. We need to calculate how much Mr Thomas would save per chair.
In other ways, he could buy a group of two or a group of five, but if he buys a group of five, it’ll work out cheaper per chair. So, we need to work out how much each chair will cost if he pays the two different prices and then find the difference. To find the price per chair, we need to divide the total amount that the shop is charging by the number of chairs that they’re giving away.
In other words, if a pair of chairs costs 344 dollars, we need to divide 344 by two to find out the price of one chair. We can do this using a written method, but there’s also a quick mental method we could use. We’ll go through the written method first. And then, we’ll use the mental method as a way to check our answer.
The written method is to use short division. How many twos are there in 344? Let’s start with the first digit. How many twos are there in three? We know there’s one lot of two in three. Now, we have a remainder of one, so we can write a small one next to the next digit.
How many twos are in 14? We know that seven times two equals 14. So, we can write seven at the top. And this time it makes the number exactly, so there’s no remainder. And finally, how many twos in four? Two times two equals four. And so, if Mr Thomas pays 344 dollars for a pair of office chairs, the cost per chair will work out as 172 dollars.
We did say there was a quick mental method we could also use. Let’s check our answer using this. To divide 344 by two, we can first partition it to help. Let’s think of it as 300 and also 44. We can halve both these numbers quickly. Half of 300 is 150. And half of 44 is 22. So, to find half of 344, we just need to add 150 and 22, which is 172.
Let’s think about the discount price now. 770 dollars will buy you five chairs. So, how can we work out what one chair will cost? We can divide 770 by five. Again, there’s a quick mental method we could use to find the answer. But let’s go through the written method and then use the mental method as a way to check how many fives are there in 770.
Let’s start with the first digit. How many fives are there in seven? There’s one five in seven, and there’s a remainder of two. So, we’ll write the two next to the next digit. How many fives are there in 27? Five, 10, 15, 20, 25 is as close as we’re going to get. So, that’s five fives. There are five fives in 27, and there’s another remainder of two. So, we’ll write that next to the next digit.
Finally, how many fives are in 20? Five, 10, 15, 20, there are four fives in 20. So, it seems that if Mr Thomas pays the discount price, each chair is going to cost 154 dollars. We can see now why it’s a discount price.
Now, we did say there was a quick mental method we could use. So, let’s go through that to check our answer. We know that when we divide a number by 10, the digits shift one place to the right. So, 770 becomes 77. But we don’t want to divide by 10. We want to divide by five, so we simply need to double 77. Double 70 is 140, and double seven equals 14. 140 plus 14 equals the answer that we got, which was 154.
So, we can see that the discount offer is cheaper. Now, all we have to do is to calculate how much Mr Thomas will save if he purchased the offer. We need to find the difference between the two prices per chair. Let’s count up from 154 to 172 to find out what the answer is. If we add six to 154, it takes us to the next multiple of 10, which is 160. And then, we can see that to get from 160 to 172 is a jump of 12. So, altogether, we’ve added an 18.
We calculated the price per chair for each of the prices that the office store was charging. We then found the difference between these two prices per chair to find how much Mr Thomas would save per chair if he purchased the discount offer. And he has a saving of 18 dollars per chair.