Question number 19. At a supermarket there are two rows of tightly packed identical shopping carts. The first row is made up of 10 carts and is 2.9 meters long, and the second row is made up of 20 carts and is 4.9 meters long. What is the length of a single shopping cart? So here in the diagram on the right we have several shopping carts, looks like there are 4 here, and if we had 10 of them in a row, let me copy here the 4, and then at the end of the row we would have the last 4, here in between let me just write dot dot dot, so altogether there are 10 carts, but we notice that the overall length is made up of two different quantities. We have the length of the first shopping cart, like so, which is what we're trying to discover, to compute, so let's call that x, and then what we have next after that is the distance between consecutive handles on a shopping cart, so let's call that y. So together what we have is x plus 9y, because altogether that's 10 carts, and that is equal to, in length, 2.9 meters, so that's one equation, and if we stack 20 carts together, what we end up looking at is a similar picture, but now with a total of 20 carts, the first cart will still be fully exposed, so it's length x together with now, not 9, but 19y, that will be equal to 4.9 meters, and then what we do is solve this system of equations, so that again, the first equation is for 10 carts, and the second equation is for 20 carts. Then let's subtract, and what we obtain is, on the left-hand side, x minus x, plus 9y minus 19y, and that would be equal to 2.9 minus 4.9, so we end up looking at minus 10y equal to negative 2, and then dividing by 10 on both sides, we see that y is equal to 0.2 meters, like that, and therefore, x is equal to, taking the first equation, for example, 2.9 minus 9 times 0.2, that gives us 2.9 minus 1.8, and so that is 1.1 meters, that's equal to x, the length of the shopping cart. So that is our answer, that's what we were looking for, y is the distance between the handles, but the entire body of the shopping cart, that is x, that comes out to 1.1 meters, and so the answer is here, c.

shopping carts

length calculation

system of equations

cart length

gap between handles