Question

Juan bought 4 pounds of chocolate
and 2 pounds of peanuts for $16. At
the same store, Jean bought 2
pounds of chocolate and 3 pounds
of peanuts for $12. What is the price
of one pound of chocolate?

Answer 1

Answer:

Step-by-step explanation:

This is a system of equations.  The 2 equations are:

4c + 2p = 16

2c + 3p = 12

Let's get rid of the p's first.  Do this by multiplying the first equation by -3 and the second equation by 2 to get a new system that looks like this:

-12x - 6p = -48

 4c + 6p =  24

Now add to get

-8c = -24 and

c = 3

That means that chocolate is $3 per pound.  Now sub that back in to either one of the original equations to get the price for peanuts:

4(3) + 2p = 16 and

12 + 2p = 16 and

2p = 4 so

p = 2

The price for peanuts is $2 per pound.

Answer 2

The price  of one pound of chocolate is $3

• Let the price of one chocolate be x

• Let the price of one peanut  by y

If Juan bought 4 pounds of chocolate and 2 pounds of peanuts for $16, this is expressed as:

4x + 2y = 16 .................... 1

If at  the same store, Jean bought 2  pounds of chocolate and 3 pounds  of peanuts for $12, this is also expressed as:

2x + 3y = 12 ........................2

Solve both equations simultaneously;

4x + 2y = 16 .................... 1 * 3

2x + 3y = 12 ........................2 * 2

_____________________________________

12x + 6y = 48 ...................... 3

4x + 6y = 24 ........................4

Subtract both expressions

12x - 4x = 48 - 24

8x = 24

x = 24/8

x = 3

Hence the price  of one pound of chocolate is $3

Learn more on simultaneous equations here: https://brainly.com/question/15165519