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The Nutty Professor sells cashews for $7.20 per pound and Brazil nuts for $4.10 per pound. How much of each type should be used to make a 32 pound mixture that sells for $5.75 per pound?



Answer :

They have to use 17.03 pounds of cashews and 17.03 pounds of nuts to make a 32 pounds mixture that sells for $5.75 per pounds

The cost of cashews per pounds = $7.20

The cost of nuts per pounds = $4.10

Consider the number of pounds of cashews as x and number of pounds of nuts as y

Total pounds of mixture = 32 pounds

The equation will be

x+y = 32

x = 32-y

Cost of the mixture for one pound = $5.75

Cost of the mixture for 32 pounds = 32×5.75

= $184

Then the equation will be

7.20x+4.10y = 184

Here we have to use the substitution method

Substitute the value of x in the equation

7.20(32-y)+4.10y = 184

230.4-7.20y+4.10y = 184

230.4-3.1y  = 184

-3.1y = 184-230.4

-3.1y = -46.4

y = 14.97 pounds

x+y = 32

x+14.97 = 32

x = 17.03 pounds

Hence, they have to use 17.03 pounds of cashews and 17.03 pounds of nuts to make a 32 pounds mixture that sells for $5.75 per pounds

Learn more about substitution method here

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