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

If 5/2 𝑎 + 4/3 𝑏 = 12, what is the value of 15𝑎 + 8𝑏?

02:24

### Video Transcript

If five over two 𝑎 plus four over three 𝑏 is equal to 12, what is the value of 15𝑎 plus eight 𝑏?

So if we’re looking to solve this problem, the first thing we want to do is we want to remove the fractions because then we’ll be able to see how we can get to 15𝑎 plus eight 𝑏. So to be able to get rid of our fractions, what we need to do is find the least common multiple of two and three.

And to do that, what we can do is we can list the first few multiples. So for two, we have two, four, six, eight. For three, we have three, six. And we see that six is the least common multiple because it’s in both of the lists of our times tables for two and three. And now we found the least common multiple, what we’re gonna do is multiply our whole equation by six. Because if we do this, what we’re going to do is remove the fractions because we’re gonna create a whole number coefficient for 𝑎 and 𝑏.

What we’ll remember though is if you’re multiplying the whole equation, that means the whole equation, so that means multiply the left-hand side by six and the right-hand side by six. So we’re gonna get 30 over two 𝑎. And we get that because we have five multiplied by six is 30 and then 30 over two 𝑎 plus 24 over three 𝑏. Again, six multiplied by four is 24, so 24 over three 𝑏, and then is equal to 72. And that’s because six multiplied by 12 is 72.

And we can do that quite easy with some mental arithmetic because if we multiply six by 10, it’s 60. Six by two is 12. Add them together, we get our 72. Well, now what we’ve done is we’ve divided. So we’ve got 30 divided by two which gives us 15. So we got 15𝑎 plus and we got 24 divided by three. So that’s eight. So we get eight 𝑏 is equal to 72.

Well, if we take a look at what we’ve got, we can see that the 15𝑎 plus eight 𝑏 is what we’re looking to find the value of in the question. So therefore, we can say that if five over two 𝑎 plus four over three 𝑏 is equal to 12, the value of 15𝑎 plus eight 𝑏 is 72.