Question

Clint is making a10-Lb bag of trail mix for his upcoming backpacking trip. The chocolate cost $3.00 per pound and mixed nuts cost $7.00 per pound and Clint has a budget of $5.80 per pound of trail mix. Using the variables c and n to represent the of pounds of chocolate and the number of pounds of nuts he should use respectively, determine a system of equations that describes the situation.Enter the equations below separated by a comma.How many pounds of chocolate should he use?How many pounds of mixed nut should he use?

Answer 1

10 = c + n, 58 = 3c + 7n

Pounds of chocolate used is 3Lb

Pounds of mixed nut used is 7 Lb

Step-by-step explanation:

a) Total pound of trail mix = 10Lb

The cost of chocolate per pound = $3.00

The cost of mixed nuts per pound = $7.00

The budget of trail mix per pound = $5.80

let c represent the pound of chocolate used

let n represent the pound of mixed nut used

Total pound of trail mix = pound of chocolate used + pound of mixed nut used

10 = c + n .....(equation 1)

Total amount for the trail mix:

The budget of trail mix per pound(Total pound of trail mix) = The cost of chocolate per pound (pound of chocolate used) + cost of mixed nuts per pound (pound of mixed nut used)

5.8(10) = 3(c) + 7(n)

58 = 3c + 7n ....(equation 2)

The equations seperated by a comma:

10 = c + n, 58 = 3c + 7n

b) To determine the pounds of chocolate he should use, we will solve the system of equations

10 = c + n

58 = 3c + 7n

from equation 1, c = 10 - n

substitute 10 - n for c in equation (2):

58 = 3(10 - n) + 7n

58 = 30 - 3n + 7n

58 = 30 + 4n

58 - 30 = 4n

28 = 4n

divide both sides by 4:

28/4 = 4n/4

n = 7

substitute for n in equation 1:

10 = c + 7

10 - 7 = c

c = 3

Pounds of chocolate used is 3Lb

Pounds of mixed nut used is 7 Lb