Applications with Systems of Equations Homework

Question

A store owner wants to develop a new snack mix by mixing chocolate and trail mix. How many pounds of chocolate costing $15.70 per pound should be mixed with 20 pounds of trail mix costing $2.60 per pound to create a mixture worth $6.97 per pound.

Answer 1

Let x be the mass of chocolate in pounds.

x pounds of chocolate cost $15.70x

20 pounds of trail mix cost $2.60 * 20 = $52

Thus the total cost of new snack mix is $52 + $15.70x

The weight of the next snack mix is x + 20 pounds, and at the target cost of $6.97/pound the total cost will be (x+20) * $6.97

Now we can write the equation

$52 + $15.70x = (x+20) * $6.97

solving for x as follows

x ($15.70-$6.97) = 20*$6.97 - $52

x * $8.73 = $87.4

x = 10 (pounds of chocolate)

Now let us check our work

10 pounds of chocolate + 20 pounds of trail mix = 30 pounds of snack mix

10 pounds of chocolate cost $157 + 20 pounds of trail mix cost $52 = 30 pounds of snack mix which cost $209

one pound of trail mix would cost $209 / 30 = $6.97

Answer 2

15.7x + 2.6(20) = 6.97(x+20)

15.7x - 6.97x = (6.97-2.6)(20 = 4.37)(20)

8.73x = 87.4

x = 87.4/8.73 = about 10 pounds of $15.70

mixed with 20 pounds of $2.60

to get 30 lbs of $6.97

15.7 is within 8.73 of 6.97

2.6 is within 4.37 of 6.97

8.73/4.37 = about 2

you need about twice as much of 2.6 as 15.7

10 lbs of $15.70 mixed with 20 lbs of $2.60

yields 30 lbs of $6.67 mix