SAT Math: 5:2 Peanut-Cashew Mixture Question

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SUMMARY

The problem involves a mixture of peanuts and cashews with a weight ratio of 5:2. In a total of 4 pounds of this mixture, the correct calculation reveals that there will be approximately 1.14 pounds of cashews. The solution requires scaling the original ratio of 7 pounds (5 pounds of peanuts and 2 pounds of cashews) down to 4 pounds while maintaining the ratio. This is achieved by multiplying the quantities by a factor of 4/7.

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Homework Statement


In a Mixture of peanuts and cashews, the ratio by weight of peanuts to cashews is 5 to 2. how many pounds of cashews will there be in 4 pounds of this mixture?


Homework Equations





The Attempt at a Solution



I used 5/2 as seven pounds in the original ratio.

Then I tested out some numbers for 2, such as 1.2, 1.4 and they all added up to a number close to four. I didn't reaaly know how to set the problem up so I ended up getting it wrong. I got 1.2.
 
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I'm said:
I used 5/2 as seven pounds in the original ratio.
Nothing wrong with thinking that 5 lbs of peanuts plus 2 lbs of cashews = 7 lbs.

To reduce 7 lbs to 4 lbs, what would you multiply by? Multiply all quantities by the same number to retain the 5/2 ratio.
 
I just got it out of insight from your reply. Thank you.
 

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