DIY Shop A sells dry play sand in 10-kilogram bags for one pound 20. DIY Shop B sells dry play sand in bags of nine pounds eight ounces for 54p. Michael wants to fill a sandpit and needs to buy a total of 370 pounds of sand. He only wants to visit one shop. Use one kilogram equals 2.2 pounds and 16 ounces equals one pound. Which shop gives the better value, A or B?
Since Michael needs 370 pounds of sand, we need to find out how many pounds this 10-kilogram bag weighs. One bag weighs 10 kilograms. If every kilogram is 2.2 pounds, then to find out how many pounds 10 kilograms is, we multiply 10 by 2.2, which will equal 22 pounds.
Each bag in Shop B weighs nine pounds eight ounces. The nine pounds’ part is fine, but we need to convert these eight ounces to pounds. 16 ounces equals one pound. And I recognize that eight ounces is half of 16. 16 divided by two equals eight. And if we divide one pound by two, one divided by two is one-half. Eight ounces is half a pound. We could write this as nine and one-half pounds. In this case, it’s probably more useful for us to write it as a decimal, 9.5 pounds.
At this point, we know how much each bag weighs in pounds. What we need to do next is find out how many of those bags Michael would need to buy. Since Michael needs 370 pounds and each bag at Shop A weighs 22 pounds, dividing 370 by 22 tells us how many of those bags we need to equal 370 pounds. 370 divided by 22 equals 16.81 repeating. But Michael can’t go to the shop and buy 0.81 repeating parts of a bag. So we need to round.
With questions like these, we always will round up. In order for Michael to have enough sand, he needs 17 bags. If he bought 16 bags, he would have slightly less than 370 pounds of sand. If he buys 17 bags, he’ll have slightly more than 370 pounds of sand.
We’ll follow the same procedure for Shop B, 370 pounds divided by 9.5 pounds per bag. When we do that, we get 38.94 continuing. Again, we can’t buy part of a bag. We need more than 38. And that means that Shop B, Michael would need to buy 39 bags.
Now that we know how many bags Michael needs from Shop A and Shop B, we can calculate how much money he would spend at both shops. For Shop A, Michael needs to buy 17 bags. And each bag costs one pound 20. So we multiply 17 by 1.20, which gives us 20 pounds and 40 pence. At Shop B, He needs 39 bags. And each bag costs 54 pence. So we multiply 39 times 0.54, which equals 21 pounds six pence.
At this point, we need to do a comparison between Shop A and Shop B. 20 pounds and 40 pence is less than 21 pounds and six pence. Michael would spend less at Shop A. Shop A is cheaper, and therefore Shop A has the better value.