The ratio of boys to girls at a winter dance is 5 to 6. If there are 90 girls, how many boys are at the dance?

75 boys

Step-by-step explanation: Our first step in this problem is to write down the unit ratio that is involved. In this case, it's boys/girls.

Next, we set up our proportion.

We know that there are 5 boys for every 6 girls.

So we have 5/6 and we're asked how many boys are at the dance if 90 girls are at the dance.

So we have .

Notice that the 99 girls must go on the bottom of the second ratio because our unit ratio tells us that we put boys/girls.

Solving from here, we use the means-extremes property.

The product of the extremes,

(90)(5) equals the product of the means, (6)(x).

So we have (90)(5) or 450 equals (6)(x) or 6x.

So we have 450 = 6x and dividing both sides by 6, 75 = x.

So 75 boys are at the winter dance.