Mathematics, 19.12.2019 23:31 rockstargirl7256

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?

Answers: 3

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Answers

Answer from: kelseeygee

The price of one pound of chocolate is $3

Let the price of one chocolate be xLet 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: link

Answer from: bcozort611

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 from: Quest

what is the answer?

Answer from: Quest

$a_1 = 1$ , and

$a_{n+1} = a_n + (n + 1)$ for $n \ge 1$

step-by-step explanation:

we can analyze the pattern at which the terms increase. let us denote $a_1 = 1$ , $a_2 = 3$ , $a_3 = 6$ , so that we can call

1 the 1st term, 3 the 2nd term, 6 the 3rd term,etc.

note the following:

from the 1st term (1) to the 2nd term (3), we go up by 2,from the 2nd term (3) to the 3rd term (6), we go up by 3from the 3rd term (6) to the 4th term (10), we go up by 4, andfrom the 4th term (10) to the 5th term (15), we go up by 5.

the pattern: to get the next term value, we just add the next term number (e.g. 1st, 2nd, to the previous term value (term values are the given numbers in the question, 1, 3, 6, 10, 15,

from $a_1 = 1$ , to get to $a_2 = 3$ , we add $2(=1+1)$

from $a_2 = 3$ , to get to $a_3 = 6$ , we add $3 (=2+1)$

etc.

we need to form a recursive formula, a formula that has the next term as a function of the previous term. so a possible recursive formula can be

$a_1 = 1$ , and $a_{n+1} = a_n +(n + 1)$ for $n \ge 1$

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Juan bought 4 pounds of chocolate
and 2 pounds of peanuts for $16. at
the same store, je...