Jess and Molly each have some marbles. Their marbles weigh a total of 810 grams. Each marble has the same mass. Molly has 11 marbles and they weigh 495 grams. How many marbles does Jess have?
With questions like this, it’s always a good idea to draw a diagram and summarize what you know. We’ve got Jess and we’ve got Molly. We don’t know how many marbles Jess has got, but we do know that Molly’s got 11. And, we know that the total mass of Molly’s marbles is 495 grams. And, we don’t know the mass of Jess’s marbles.
Okay, as diagrams go, this isn’t a very pretty one. It’s more like a table. But hopefully, it does help us organize our thinking. For example, we can add another column for the total number of marbles, and that’s gonna help us to work out some of the missing values. We don’t know how many marbles there are in total, but we do know that the total mass of the marbles is 810 grams.
To get that total mass of marbles of 810 grams, we’d need to add the mass of Jess’s marbles to the mass of Molly’s marbles. Let’s use the letter 𝑥 to represent the total mass of Jess’s marbles. So, we know that 𝑥 plus 495 is equal to 810. We’ve got an equation. And, if we subtract 495 from each side of that equation, we’ll have an expression for 𝑥. That means we’re going to have to calculate the value of 810 minus 495.
And, we could use a column method to calculate that. Zero minus five, well, we can’t do that, so we’re gonna have to borrow one from the tens column. So, that gives us 10 minus five which is five. Now, moving on to the tens column, zero minus nine. Well, we can’t do that. We’re gonna have to borrow one from the hundreds column. And, that leaves us with 10 minus nine which is one. And, moving on to the hundreds column, seven minus four is three. So, 𝑥 is 315, or the mass of Jess’s marbles is 315 grams.
Now, if we let 𝑚 represent the mass of one marble, we know that 11 times 𝑚 is 495 grams. 11 marbles weigh 495 grams. So, if I can calculate how many times 11 goes into 495, I’ll know the mass of one marble. Right then, 11s into four don’t go, but 11s do go into 49 four times because four times 11 is 44.
Now, we can subtract 44 from 49. Nine take away four is five. And, four take away four is zero. So, 11s go into 49 four times remainder five. So, we can bring down the five. And, we’ve got to work out, how many times does 11 go into 55? Well, it’s five times because five times 11 is 55. Now, 55 minus 55 is zero. That means that 11s go into 55 five times with no remainder. This means that one marble has a mass of 45 grams.
If I multiplied 45 by 11, I’d get 495. This tells me that however many marbles Jess has got, if I multiply that by 45 grams, I get 315 grams. So, if I do the calculation 315 divided by 45, that will tell me the number of marbles that Jess has. Well, this is a slightly tricky calculation to do because 45s don’t go into three. 45s don’t go into 31. So, we’ve just more or less got to go straight to the answer, how many times does 45 go into 315? Let’s try and think of some other ways of doing this calculation.
I could write 315 divided by 45 as a fraction like this. Then, I can start looking for some factors. Well, I know that three times 100 is 300 and three times five is 15. So, three times 105 is 315. On the denominator, three times 15 is 45. I can cancel the threes. And, I’ve got an equivalent fraction, 105 over 15. Now, both the numerator and denominator end in five, so they must be multiples of five. Well, five times three is 15 on the denominator. And, I know that five times 20 is 100, so 105 must be 21 lots of five. Great, now I can cancel the fives. And, I should know from my times tables that 21 divided by three is seven. This means that Jess has got seven marbles because seven times 45 is 315.
So, let’s just recap what we’ve done. First, we used the information in the question to work out that Jess’s marbles weighed a total of 315 grams. Then, we worked out that Molly’s 11 marbles weighed a total of 495 grams. So, each one must have weighed 45 grams. And finally, we worked out how many times 45 went into 315 to work out how many marbles that Jess has. Now, there are different ways that you could have tackled each of those steps, but you should always come to the same answer that Jess has seven marbles.