Question

A store is having a sale on chocolate chips and walnuts. For 5 pounds of chocolate chips and 3 pounds of walnuts, the total cost is $25 . For 7 pounds of chocolate chips and 9 pounds of walnuts, the total cost is $53 . Find the cost for each pound of chocolate chips and each pound of walnuts.

Answer 1

Answer:

one pound of chocolate chips = $2.75

one pound of walnuts = $3.75

Step-by-step explanation:

we can solve this by first making an equation

let's write the number of chocolate chips in c

and the number of walnuts in w

5c  + 3w = 25

7c + 9w = 53

let's first solve for c by multiplying the top equation by 3 and subtracting the bottom equation from it

(15c + 9w = 75) - (7c + 9w = 53)

8c = 22

c = $2.75

Let's now start to solve for w by inputting c into one of the equations.

(2.75)7 + 9w = 53

19.25 + 9w = 53

9w = 53 - 19.25

9w = 33.75

w = $3.75

a pound of chocolate chips  = 2.75

a pound of walnuts = 3.75

give me brainliest, please!

Hope this helps :)

Answer 2

Answer:

each pound of chocolate chips costs $2.75

each pound of walnuts costs $3.75

Step-by-step explanation:

let c be the cost of a pound of chocolate chips

and w be the cost of a pound of chocolate chips

For 5 pounds of chocolate chips and 3 pounds of walnuts,

the total cost is $25  means  5c + 3w = 25

For 7 pounds of chocolate chips and 9 pounds of walnuts,

the total cost is $53  means  7c + 9w = 53

Now we have to solve the system:

$\begin{cases}5c+3w=25&\\ 7c+9w=53&\end{cases}$

$\Longleftrightarrow \begin{cases}15c+9w=75&\\ 7c+9w=53&\end{cases}$

$\Longleftrightarrow \begin{cases}15c+9w=75&\\ 8c=22&\end{cases}$

$\Longleftrightarrow \begin{cases}15c+9w=75&\\ c=\frac{11}{4} &\end{cases}$

$\Longleftrightarrow \begin{cases}9w=75-15 \times \frac{11}{4} &\\ c=\frac{11}{4} &\end{cases}$

$\Longleftrightarrow \begin{cases}9w=\frac{135}{4} &\\ c=\frac{11}{4} &\end{cases}$

$\Longleftrightarrow \begin{cases}w= \frac{15}{4} &\\ c=\frac{11}{4} &\end{cases}$