Video: SAT Practice Test 1 • Section 4 • Question 3

Monica walked into a supermarket to buy ice cream and chocolate. The price of one ice cream cone is 2 dollars, and that of one bar of chocolate is 5 dollars. Monica bought 6 items from the supermarket and paid 18 dollars in total. How many ice cream cones did she buy?

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Video Transcript

Monica walked into a supermarket to buy ice cream and chocolate. The price of one ice cream cone is two dollars, and that of one bar of chocolate is five dollars. Monica bought six items from the supermarket and paid 18 dollars in total. How many ice cream cones did she buy?

So to solve this problem, what we’re gonna need to do is set up some equations. And to help us do that, what I’m gonna do is I’m gonna call the number of ice cream cones 𝑥 and the number of chocolate bars 𝑦.

So to set up our first equation, I’m gonna use these three bits of information. The price of one ice cream cone is two dollars. The price of one chocolate bar is five dollars. And that she paid 18 dollars in total. So therefore, we can say that two 𝑥, because two multiplied by the number of ice cream cones which we’ve called 𝑥, plus five multiplied by 𝑦, or five 𝑦, is gonna be equal to 18. And I’ve called this equation one and I’ve labelled it so. I do that so it’s easier to talk about what we’re gonna do as we move through the question.

Now next, what I’m gonna do is use this piece of information. And this piece of information is that Monica bought six items in total. So therefore, I can set up the equation 𝑥 plus 𝑦 is equal to six. And I’m gonna call this equation two.

So now what we have is a pair of simultaneous equations. So in order to solve this, what I’m gonna do is I’m gonna use the substitution method. But to enable me to be able to do this, what I need to do is rearrange one of our equations. And in this case, I’m gonna rearrange equation two.

And what I’m gonna do to rearrange equation two is subtract 𝑦 from each side of the equation. And I’m gonna do this to make 𝑥 the subject. I could’ve made 𝑦 the subject. I’ve just happened to have chosen to make 𝑥 the subject. When I do that, I get 𝑥 is equal to six minus 𝑦.

And now what this leads me to is the next stage where I’m gonna substitute 𝑥 equals six minus 𝑦 into one. So I’m gonna swap any of my 𝑥-values for six minus 𝑦. And when I do that, I get two multiplied by six minus 𝑦 plus five 𝑦 is equal to 18.

Now the next stage is to distribute my two over my parentheses. And to do that, what I do is multiply two by six and then two by negative 𝑦. So I’m gonna get 12 minus two 𝑦 plus five 𝑦 is equal to 18, which is gonna give me 12 plus three 𝑦 is equal to 18, because negative two 𝑦 add five 𝑦 is positive three 𝑦.

So then the next stage is to subtract 12 from each side of the equation. And when we do that, we get three 𝑦 is equal to six. And then to find single 𝑦, so the number of chocolate bars, what I’m gonna do is divide each side of the equation by three. So when I do that, I get 𝑦 is equal to two. So we know that there are two chocolate bars.

So now what we can do is use this information to find the number of ice cream cones, or 𝑥. And to do that, what we’re gonna do is substitute 𝑦 equals two into 𝑥 equals six minus 𝑦. So when we do that, we get 𝑥 is equal to six minus two. So therefore, we can say that Monica bought four ice cream cones.

And what we can do is just double-check this works. So what we can do is use our value for 𝑦, which is two, and our value for 𝑥, which is four, and substitute them back into equation one just as a quick check. And if we do that, we get two multiplied by four plus five multiplied by two is equal to 18. Well, this gives us eight add 10 is equal to 18, which is correct. So therefore, we can definitely say that Monica bought four ice cream cones.

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