Question

Clint is making a 10-lb bag of trail mix for his upcoming backpacking trip. Thechocolates cost $3.00 per pound and mixed nuts cost $6.00 per pound and Clint has abudget of $5.10 per pound of trail mix. Using the variables c and n to represent thenumber of pounds of chocolate and the number of pounds of nuts he should userespectively, 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 nuts should he use? Pls see the picture

Answer 1

Since c represents the number of pounds of chocolates

Since n represents the number of pounds of nuts

Since Clint is making 10 pounds of them, then

`c+n=10\rightarrow(1)`

Since the cost of 1 pound of chocolates is $3.00

Since the cost of 1 pound of nuts is $6.00

Since the Clint budget is $5.1 per pound, then

`10*5.1-\text{ \$51}`

Multiply c by 3 and n by 6, then add the products and equate the sum by 51

`\begin{gathered} 3(c)+6(n)=5.1 \\ 3c+6n=51\rightarrow(2) \end{gathered}`

The system of equations is

c + n = 10

3c + 6n = 51

Let us solve them

Multiply equation (1) by -3 to make the coefficient of c equal in values and different in signs

`\begin{gathered} -3(c)-3(n)=-3(10) \\ -3c-3n=-30\rightarrow(3) \end{gathered}`

Add equations (2) and (3)

`\begin{gathered} (3c-3c)+(6n-3n)=(51-30) \\ 0+3n=21 \\ 3n=21 \end{gathered}`

Divide both sides by 3 to find n

`\begin{gathered} (3n)/(3)=(21)/(3) \\ n=7 \end{gathered}`

Substitute n by 7 in equation (1)

`c+7=10`

Subtract 7 from both sides

`\begin{gathered} c+7-7=10-7 \\ c=3 \end{gathered}`

He should use 3 pounds of chocolate

He should use 7 pounds of nuts

If his budget is $51