Planters peanut company wants to mix 20 0f peanuts worth $3 a pound with cashews worth $5 a pound in order to make a mix worth $3.50 a pound. How many pounds of cashews should be added to the peanuts?
Make this chart, putting in the data given and letting x be the number
of pounds of cashews:
pounds | price/pound | money taken in if all sold
Peanuts 20 lb | $3 |
Cashews x lb | $5 |
----------------------------------------------------------
Mixture | $3.50 |
The number of pounds of mixture is expressed by adding 20 pounds
and x pounds, getting 20+x pounds
pounds | price/pound | money taken in if all sold
Peanuts 20 lb | $3 |
Cashews x lb | $5 |
----------------------------------------------------------
Mixture 20+x lb | $3.50 |
The money that would be taken in if all 20 lbs. of peanuts were
sold separately is found by multiplying the price per pound by
the number of pounds of peanuts. That's 20 lb times $3. So we
fill that in as 3*20 or $60.
The money that would be taken in if all x lbs. of cashews were
sold separately is found by multiplying the price per pound by
the number of pounds of cashews. That's $5 times x lbs. So we
fill that in with $5x.
The money that will be taken in when all 20+x lbs. of mixture are
sold is found by multiplying the price per pound of mixture by
the number of pounds. That's $3.50 times (20+x) lbs. So we fill that in
with $3.50(20+x).
pounds | price/pound | money taken in if all sold
Peanuts 20 lb | $3 | $3*20 = $60
Cashews x lb | $5 | $5*x = $5x
----------------------------------------------------------
Mixture 20+x lb | $3.50 | $3.50(20+x)
The equation is gotten from the last column. That is,
The money that would be taken in if the peanuts were sold
separately, which is $3*20 or $60
PLUS
The money that would be taken in if the cashews were sold
separately, which is $5*x or $5x
EQUALS
The money that will be taken in when all the mixture is
sold, which is $3.50(20+x)
So the equation is
$3*20 + $5*x = $3.50(20+x)
60 + 5x = 3.50(20+x)
Solve that and get:
or 
lbs. of cashews.
Edwin
