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Re: The ratio of the number of boys to the number of...
Let b the number of boys, and g the number of girls. b/g=2/7 => 7b=2g g=b+250 7b=2(b+250)=2b+500 5b=500 ==> b=100 g=b+250=100+250=350 Verification: 100/350=10/35=2/7
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A class consists of 16 kids, 6 boys and 10 girls.
Emily questioned all the students and discovered that
8 out of 10 girls prefer valentines day over birthdays, but only 2 out of 6 boys prefer valentines day over birthdays.
What is the ratio of children in the class that prefer valentines day over birthdays.
If there are 40 total students, and 25 are boys, then (40-25) of them are girls, or 15. That means the ratio of boys to girls is 25 to 15, or 25/15 This can be simplified by dividing by 5, so the ratio is 5/3
If there are 25 boy in a class of 40 pupils, there are 40 - 25 = 15 girls. The ratio of boys to girls hence is 25:15, or as reduced fraction 5:3 = 1.6666...
The best way to solve this is to develop one or more equations and then solve for the unknown numbers.
I solved this problem twice using different sets of equations to make sure I was right, and here is what I found:
1) I used the equations x + y = 623, and x = (2/3)y. In these equations, x is the number of girls and y is the number of boys. Substituting the second equation into the first, I get (2/3)y + y = 623. Adding the left side together I get : (5/3)y = 623. Dividing both sides by (5/3) I get 373.8. This means that x (the number of girls) is 249.2.
2) For the second attempt, I developed the equation: 2x+3x=623. Here 2x is the number of girls, and 3x is the number of boys. Adding the left side I get: 5x = 623. Dividing both sides by 5 I get: x = 124.6. This means that the number of girls (2x) is 249.2. Just like in the first method.
But since you can't have a 1/5 of a girl, the answer must be 249 girls.
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