The ratio of girls to boys in the junior high band is 5 to 7. At the beginning of the year, there were 72 students in the band. By the end of the year, the ratio of girls to boys was 3 to 4. If there are now 48 in the band, how many girls joined the band during the school year.
The language is very confusing in its use of present and past tenses.
When is "now"? The end of the year?
If girls joined the band, how come there are now fewer students than at the beginning?
I cannot believe the question was posed as you state. If so, the problem is poorly constructed.
At the start of the school year for this question it should give us how many girls and boys here are and the total there is AND at the end of the school year the number dropped so what do mean by "joined"?No one obviously joined if boys left and 48 was the remender then thats fair BUT IT DIDNT SAY BOYS LEFT if they said that it would go something like "throughut the school year boys left band leaving 48 at the end of the school year however many girls joined"
something around the lines of that!
"now"? it seems like they are implying there is a change
if it was the same through out the year why put now? it confused me after even finding the answer
not really but finding the idea to solving it now is making me think there is something else and I Don't want to miss this question because i was mis guided or "blind".
I'm asking for help on this because they think a normal 6th grader can solve this because if they dislike reading or not very good at it this already hard and the way they write makes me confused especially this "By the end of the year, the ratio of girls to boys was 3 to 4. If there are now 48 in the band, how many girls joined the band during the school year."ITS CONFUSING!!
The question is stating that at the end of the year there are 48 boys and they are asking for the number of girls that joined the band. So, first we need to figure out the amount of girls and boys to begin with...
ratio is 5:7 and there are 72 students in the class.
to break this down I added the 5+7=12 so there are a total of 12 students in a group. I divided 72/12=6 groups of students.. so there were 30 girls to begin with and 42 boys in the classroom.
Second part states the ratio is now 3:4 with 48 boys in the classroom.
3 girls x
4 boys 48 boys
we are solving for x so 48/4 =12 and 3*12=36 so there are now 36 girls in the band.. six girls joined.
I hope this helped
To solve this problem, we can set up a system of equations based on the given information.
Let's say the number of girls at the beginning of the year is 5x, and the number of boys is 7x (according to the ratio 5:7). Therefore, the total number of students at the beginning of the year is 5x + 7x = 12x.
Similarly, at the end of the year, the number of girls is 3y, and the number of boys is 4y (according to the ratio 3:4). So, the total number of students at the end of the year is 3y + 4y = 7y.
We know that there are 72 students at the beginning of the year, so we can set up the equation:
12x = 72
Now, let's find the value of x:
x = 72 / 12
x = 6
Therefore, at the beginning of the year, there were 5x = 5 * 6 = 30 girls in the band, and 7x = 7 * 6 = 42 boys.
We also know that at the end of the year, the total number of students is 48, so we can set up the equation:
7y = 48
Now, let's find the value of y:
y = 48 / 7
y ≈ 6.857
Since we can't have a fraction of a student, we need to round y to the nearest whole number. Therefore, y = 7.
Now, we can find the number of girls who joined the band during the school year:
Number of girls joined = 3y - 5x
= 3 * 7 - 3 * 6
= 21 - 18
= 3
Therefore, 3 girls joined the band during the school year.