c+p = 60
4.00c + 2.50p = 3.00*60
Now just solve for c and p
The modern grocery has cashews that sell for $4.00 a pound and peanuts that sell for 2.50 a pound. How much of each must Albert the grocer mixed to get 60 pounds of mixture that he can sell for three dollars per pound? Express the problem as a system of linear equations and solve using the method of your choice
3 answers
How do you solve this
well, since c+p=60,
p = 60-c
4.00c + 2.50(60-c) = 3.00*60
That is, add up the values of the separate nuts, and it must equal the value of the final mixture.
4.00c + 150 - 2.5c = 180
1.5c = 30
c = 20
So, 20 lbs cashews and 40 lbs peanuts
Note that since the final cost of $3.00 is 2/3 of the way from $4.00 to $2.50, the amount of peanuts is 2/3 of the total.
p = 60-c
4.00c + 2.50(60-c) = 3.00*60
That is, add up the values of the separate nuts, and it must equal the value of the final mixture.
4.00c + 150 - 2.5c = 180
1.5c = 30
c = 20
So, 20 lbs cashews and 40 lbs peanuts
Note that since the final cost of $3.00 is 2/3 of the way from $4.00 to $2.50, the amount of peanuts is 2/3 of the total.
3 answers