Ratio problem: finding boys last year given girl ratio changes

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teddunner
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I'm at a loss. I can't figure it out. Please help.

Last year's 6th grade boy to girl ratio was 3 to 4. This year's 6th grade boy to girl ratio is 5 to 6. If the total number of students were the same this year as they were last year; what is the number of 6th grade boys last year if there are 96 girls this year?
 

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teddunner said:
I'm at a loss. I can't figure it out. Please help.

Last year's 6th grade boy to girl ratio was 3 to 4. This year's 6th grade boy to girl ratio is 5 to 6. If the total number of students were the same this year as they were last year; what is the number of 6th grade boys last year if there are 96 girls this year?

(Wave)

Let $\text{boys_1}$ be the number of boys of last year's 6th grade, $\text{girls_1}$ the number of girls of last year's 6th grade, $\text{boys_2}$ the number of boys of this year's 6th grade and $\text{girls_2}$ the number of girls of this year's 6th grade.

Then the following relations hold:

$$\frac{\text{boys_1}}{\text{girls_1}}=\frac{3}{4}$$

$$\frac{\text{boys_2}}{\text{girls_2}}=\frac{5}{6}$$

$$\text{boys_1}+\text{girls_1}=\text{boys_2}+\text{girls_2}$$

We are looking for the value of $\text{boys_1}$.

We are given that $\text{girls_2}$ is equal to $96$.

So, $\text{boys_2}=\frac{5}{6} \cdot 96=80$.

Also we get that $\text{boys_1}+\text{girls_1}=176$.

Can you continue?
 
evinda said:
(Wave)

Let $\text{boys_1}$ be the number of boys of last year's 6th grade, $\text{girls_1}$ the number of girls of last year's 6th grade, $\text{boys_2}$ the number of boys of this year's 6th grade and $\text{girls_2}$ the number of girls of this year's 6th grade.

Then the following relations hold:

$$\frac{\text{boys_1}}{\text{girls_1}}=\frac{3}{4}$$

$$\frac{\text{boys_2}}{\text{girls_2}}=\frac{5}{6}$$

$$\text{boys_1}+\text{girls_1}=\text{boys_2}+\text{girls_2}$$

We are looking for the value of $\text{boys_1}$.

We are given that $\text{girls_2}$ is equal to $96$.

So, $\text{boys_2}=\frac{5}{6} \cdot 96=80$.

Also we get that $\text{boys_1}+\text{girls_1}=176$.

Can you continue?

I can continue, the answer just doesn't make sense. I think it is just an error that slipped through the cracks.
 
teddunner said:
I can continue, the answer just doesn't make sense. I think it is just an error that slipped through the cracks.

Yes, I made the calculations and noticed the same. (Nod)
 
evinda said:
Yes, I made the calculations and noticed the same. (Nod)

Thank you! I was beginning to think it was just me.