Having a hard time figuring out how to even get started

[Yvette]

Here's a problem I'm trying to help my daughter with but I can't figure out how to get started (been away from pre-algebra for a while). Her school is using the singapore method with bar modeling (which I was never taught) and I'm not sure if it's applicable to this problem:

A farmer is selling his crops at the local market. 3/4 of the sales from his onions is as much as 3/5 of his sales from carrots. The sales from carrots is $240 more than the sale from onions. Find the total sales from both the onions and the carrots.​

Any help would be greatly appreciated!

 

[HallsofIvy]

Without "bars":
"A farmer is selling his crops at the local market. 3/4 of the sales from his onions is as much as 3/5 of his sales from carrots. The sales from carrots is $240 more than the sale from onions. Find the total sales from both the onions and the carrots."

Since they are asking about "onions and carrots", let x be the sales from onions and let y be the sales from carrots, both in dollars.

"3/4 of the sales from his onions is as much as 3/5 of his sales from carrots."
"3/4 of the sales from his onions" is 3/4 times x or (3/4)x and "3/5 of his sales from carrots" is 3/5 times y or (3/5) y so:

(3/4)x= (3/5)y

"The sales from carrots is $240 more than the sales from onions."
"$240 more than the sales from onions" is x+ 240 so

y= x+ 240.

Since y= x+ 240, we can replace the "y" in "(3/5)y" with x+ 240:

(3/4)x= (3/5)(x+ 240)= (3/5)x+ 3(240/5)= (3/5)x+ 3(48)= (3/5)x+ 144

Subtract (3/5) x from both sides: 3/4- 3/5= 3(5)/(4(5))- 3(4)/(5(4))= 15/20- 12/20= 3/20
so (3/4)x- (3/5)x= (3/20)x= 144.

Divide both sides by 3: (1/20)x= 144/3= 48

Multiply both sides by 20: x= 48(20)= 960
Since y= x+ 240, y= 960+ 240= 1200

Finally, write the answer in a complete sentence: "The farmer sold $960 worth of onions and $1200 worth of carrots."

Check:
"3/4 of the sales from his onions is as much as 3/5 of his sales from carrots."
3/4 of 960= 3(960/4)= 3(240)= 720 and 3/5 of 1200= 3(1200/5)= 3(240)= 720.
Yes, that is correct.

"The sales from carrots is $240 more than the sale from onions."
Sales from onions was $960= $720+ $240.
Yes, that is correct.

 

[Yvette]

Thanks!

Thanks for the help! I had some of it but not all and my daughter was lost in how to solve a problem this complicated (we haven't seen anything like this in her homework so far!). Does the bar method work for this?

Without "bars":
"A farmer is selling his crops at the local market. 3/4 of the sales from his onions is as much as 3/5 of his sales from carrots. The sales from carrots is $240 more than the sale from onions. Find the total sales from both the onions and the carrots."

Since they are asking about "onions and carrots", let x be the sales from onions and let y be the sales from carrots, both in dollars.

"3/4 of the sales from his onions is as much as 3/5 of his sales from carrots."
"3/4 of the sales from his onions" is 3/4 times x or (3/4)x and "3/5 of his sales from carrots" is 3/5 times y or (3/5) y so:

(3/4)x= (3/5)y

"The sales from carrots is $240 more than the sales from onions."
"$240 more than the sales from onions" is x+ 240 so

y= x+ 240.

Since y= x+ 240, we can replace the "y" in "(3/5)y" with x+ 240:

(3/4)x= (3/5)(x+ 240)= (3/5)x+ 3(240/5)= (3/5)x+ 3(48)= (3/5)x+ 144

Subtract (3/5) x from both sides: 3/4- 3/5= 3(5)/(4(5))- 3(4)/(5(4))= 15/20- 12/20= 3/20
so (3/4)x- (3/5)x= (3/20)x= 144.

Divide both sides by 3: (1/20)x= 144/3= 48

Multiply both sides by 20: x= 48(20)= 960
Since y= x+ 240, y= 960+ 240= 1200

Finally, write the answer in a complete sentence: "The farmer sold $960 worth of onions and $1200 worth of carrots."

Check:
"3/4 of the sales from his onions is as much as 3/5 of his sales from carrots."
3/4 of 960= 3(960/4)= 3(240)= 720 and 3/5 of 1200= 3(1200/5)= 3(240)= 720.
Yes, that is correct.

"The sales from carrots is $240 more than the sale from onions."
Sales from onions was $960= $720+ $240.
Yes, that is correct.

 

[stapel]

A farmer is selling his crops at the local market. 3/4 of the sales from his onions is as much as 3/5 of his sales from carrots. The sales from carrots is $240 more than the sale from onions. Find the total sales from both the onions and the carrots.

Set up the bars, in the manner demonstrated in the book:

parts (bars):

         *--*--*--*--*
 onions: |##|##|##|  |
         *--*--*--*--*--*
carrots: |##|##|##|  |  |
         *--*--*--*--*--*

The "parts" with the "##" are the ones marked to stand for the "as much as" stipulation. Clearly, each "part" is of equal value. Then the one "part" more of carrots than of onions must be the overage, the $240. There are 4 + 5 = 9 parts. Do the multiplication.

 

[Yvette]

Wow!

That is so much easier! I can't believe it!
I can't believe how much easier that is! Woo Hoo!

Set up the bars, in the manner demonstrated in the book:

parts (bars):

         *--*--*--*--*
 onions: |##|##|##|  |
         *--*--*--*--*--*
carrots: |##|##|##|  |  |
         *--*--*--*--*--*

The "parts" with the "##" are the ones marked to stand for the "as much as" stipulation. Clearly, each "part" is of equal value. Then the one "part" more of carrots than of onions must be the overage, the $240. There are 4 + 5 = 9 parts. Do the multiplication.