there us a ratio of 3 adults for every 7 children (3:7) and 152 more children than adults. How many adults are there?

Answer 1

Here's a video to help explain it! Excuse the writing! I need to get a new mouse! :)

Answer 2

From the info given, we can write two equations. For these equations, we will let "a" be the variable for adults and "k" be the variable for the kids.

From what is given, we know that there are 152 more kids than adults. This means that whatever number of adults there are, we can add 152 to that and find the number of kids. Therefore

k = a +152

Also, we know that the ratio of kids to adults is 7/3. Therefore

k = (7/3)a

So now we have two different equations that expresses the variable k in terms of a. We can set these equations equal to eachother

(7/3)a = a + 152

At this point, we combine like terms, in this case, the a's are the only like terms. We subtract a on the right side of the equation, which cancels out, but we also subtract a on the left side of the equation. So on the left side we have

(7/3)a - a = 152

We turn the second a into an equivalent fraction so that we can subtract the two fractions from each other

(7/3)a - (3/3)a = 152

(7/3) - (3/3) = (4/3), so now our equation is

(4/3)a = 152

Finally, we isolate a. It is currently being multiplied by the fraction (4/3), so we divide by this fraction on both sides of the equation. On the left side, it will cancel and simply equal "a", but on the right side we have

152 / (4/3)

Doing the math on this gives us 114. So our equation is now

a = 114

So know we know that the number of adults is 114. Now we input this answer into either of the original equations and we can find how many adults there are. The first equation is probably the easier of the two since it only involves addition. So we have

114 +152 = 266

Therefore there are 266 kids

We can check ourselves because if we take the number of kids and divide it by the number of adults, it should give us the fraction of (7/3), which is the same as 2.33333 (with repeating 3's) as a decimal.

If we take 266 and divide it by 114, we will indeed get 2.33333