Ratio/Percentage Question from Singapore Math

senseimichael

senseimichael

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This is pre-algebra, because the students have only been taught very basic algebra, and do not know how to manipulate them.

A chef prepared some fishballs for the guests during a birthday party. 60% of the guests were children. Among the children, the ratio of the number of girls to the number of boys is 5:3. A total of 9408 fishballs were prepared so that each adult got 5 fishballs and each child got 6 fishballs. There were no fishballs left after the party. How many boys attended the party?

I know that the ratio of boys to girls is 5:9, simply by taking the 40:60 ratio of adults to children and then doing a "person-fishball" multiplication. I got stuck after that.

For those who have no idea what they are, fishballs are yummy snacks in Singapore made of fish battered into a paste with flour and then fried or boiled. Yummy!
 
"I know that the ratio of boys to girls is 5:9, simply by taking the 40:60 ratio of adults to children and then doing a "person-fishball" multiplication."?? Didn't the problem say that "the ratio of the number of girls to the number of boys is 5:3", not 9 to 5?

Suppose there are "X" children and "Y" adults for a total of X+ Y guests. 60% of the guests are children so X= 0.6(X+ Y). Children eat six fishballs each so the children eat 6X fishballs. Adults eat five fishballs each so adults eat 5Y fishballs. Altogether they each 6X+ 5Y= 9408 fishballls.

Solve the two equations 0.4X= 0.6Y and 6X+ 5y= 9408 for X and Y. X is the number of children and "the ratio of girls to boys is 9 to 3" the number of boys is X/4.
 
senseimichael said:
This is pre-algebra, because the students have only been taught very basic algebra, and do not know how to manipulate them.

A chef prepared some fishballs for the guests during a birthday party. 60% of the guests were children. Among the children, the ratio of the number of girls to the number of boys is 5:3. A total of 9408 fishballs were prepared so that each adult got 5 fishballs and each child got 6 fishballs. There were no fishballs left after the party. How many boys attended the party?
Click to expand...
We need to avoid algebra, so let's stick with ratios and fractions.

children = 60% = 3/5 of total; adults = 40% = 2/5 of total
girls:boys = 5:3, so girls = 5/8 of children = 15/40 of total, boys = 3/8 of children = 9/40 of total

(I'm keeping a common denominator for future use.)

So girls:boys:adults = 15:9:16, with a total of 40 parts.

Each child gets 6 and each adult gets 5, so the ratio of fishballs is 15*6 : 9*6 : 16*5 = 90:54:80, with a total of 224 parts.

The girls got 90/224 of the 9408 fishballs = 3780.

I think you tried something like my last step, but messed it up somehow to get 5:9.
 
H
HallsofIvy said:
"I know that the ratio of boys to girls is 5:9, simply by taking the 40:60 ratio of adults to children and then doing a "person-fishball" multiplication."?? Didn't the problem say that "the ratio of the number of girls to the number of boys is 5:3", not 9 to 5?

Suppose there are "X" children and "Y" adults for a total of X+ Y guests. 60% of the guests are children so X= 0.6(X+ Y). Children eat six fishballs each so the children eat 6X fishballs. Adults eat five fishballs each so adults eat 5Y fishballs. Altogether they each 6X+ 5Y= 9408 fishballls.

Solve the two equations 0.4X= 0.6Y and 6X+ 5y= 9408 for X and Y. X is the number of children and "the ratio of girls to boys is 9 to 3" the number of boys is X/4.
Click to expand...

Handling simultaneous equations seems beyond pre-algebra to me...
 
Dr.Peterson said:
We need to avoid algebra, so let's stick with ratios and fractions.

children = 60% = 3/5 of total; adults = 40% = 2/5 of total
girls:boys = 5:3, so girls = 5/8 of children = 15/40 of total, boys = 3/8 of children = 9/40 of total

(I'm keeping a common denominator for future use.)

So girls:boys:adults = 15:9:16, with a total of 40 parts.

Each child gets 6 and each adult gets 5, so the ratio of fishballs is 15*6 : 9*6 : 16*5 = 90:54:80, with a total of 224 parts.

The girls got 90/224 of the 9408 fishballs = 3780.

I think you tried something like my last step, but messed it up somehow to get 5:9.
Click to expand...

Thank you, Dr Peterson sir! Your train of thought gave me the solution!

We have the starting ratio of A: C=2:3,

So with fishballs in, A:C=(2x5):(3x6)=10:18=5:9, the ratio of the number of fishballs adults get to children.

Since in total the number of fishballs is 14 units,

14 units=9408, 1 unit=672, 9 units (the number of fishballs for children)= 2268.

Now, ratio of G:B=5:3, so the total of parts of children would be 8,

8 parts=6048, 1 part=756, 3 parts (boys)=2268

Since each boy would also get 6 fishballs,

2268/6=378

378 boys!
 
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