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Question Solve a system of linear equations to find the cost per pound of walnuts and chocolate chips. For 3 lbs walnuts and 5 lbs chocolate chips, total cost is 19.For9lbswalnutsand7lbschocolatechips,totalcostis19. For 9 lbs walnuts and 7 lbs chocolate chips, total cost is 35. Find the cost per pound of walnuts: andperpoundofchocolatechips: and per pound of chocolate chips:

Studdy Solution

STEP 1

Assumptions1. The cost of walnuts and chocolate chips is linear, meaning it increases proportionally with the weight. . The total cost for3 pounds of walnuts and5 pounds of chocolate chips is 19.<br/>3.Thetotalcostfor9poundsofwalnutsand7poundsofchocolatechipsis19.<br />3. The total cost for9 pounds of walnuts and7 pounds of chocolate chips is 35.

STEP 2

Let's denote the cost per pound of walnuts as ww and the cost per pound of chocolate chips as cc. We can then write down two equations based on the given information.
w+5c=19w +5c =199w+7c=359w +7c =35

STEP 3

To solve this system of equations, we can use the method of substitution or elimination. In this case, let's use the method of elimination. We can start by multiplying the first equation by3 and the second equation by1 to make the coefficients of ww in both equations the same.
9w+15c=579w +15c =579w+7c=359w +7c =35

STEP 4

Now, subtract the second equation from the first to eliminate ww.
(9w+15c)−(9w+7c)=57−35(9w +15c) - (9w +7c) =57 -35

STEP 5

This simplifies to8c=228c =22

STEP 6

Now, solve for cc by dividing both sides of the equation by8.
c=22/8c =22 /8

STEP 7

Calculate the value of cc.
c=22/=$2.75c =22 / = \$2.75

STEP 8

Now that we have the cost per pound of chocolate chips, we can substitute cc into the first equation to find the cost per pound of walnuts.
3w+5($2.75)=193w +5(\$2.75) =19

STEP 9

implify the equation.
3w+$13.75=193w + \$13.75 =19

STEP 10

Subtract 13.75frombothsidesoftheequationtoisolate13.75 from both sides of the equation to isolate 3w$.
3w=19−$13.753w =19 - \$13.75

STEP 11

Calculate the value of 3w3w.
3w=19−$13.75=$5.253w =19 - \$13.75 = \$5.25

STEP 12

Finally, divide both sides of the equation by to solve for ww.
w=$5.25/w = \$5.25 /

STEP 13

Calculate the value of ww.
w=$5.25/3=$.75w = \$5.25 /3 = \$.75The cost for each pound of walnuts is .75andthecostforeachpoundofchocolatechipsis.75 and the cost for each pound of chocolate chips is 2.75.

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