Mathematics, 31.12.2019 11:31, GreenHerbz206

Jennifer's bill for 6 cans of grape juice and 4 cans of apple juice was $13.10. when she got home she found out that she should have bought 4 cans of grape juice and 6 cans of apple juice. although she mixed up the order, she did save 60 cents. what is the cost per can of apple and grape juice
solve the system using substitution and elimination.
convert your equations to slope intercept form and identify the variables for your x and y axes. then graph.
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Answers: 3

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answered: tytianadyson74

Part 1) The system is solved using elimination

The cost per can of grape juice is $\$1.19$ and the cost per can of apple juice is $\$1.49$

Part 2) The system is solved using substitution

The cost per can of grape juice is $\$1.19$ and the cost per can of apple juice is $\$1.49$

Part 3) The system is solved by graphing

The graph in the attached figure

Step-by-step explanation:

Part 1) Solve the system by elimination

Let

x----> the cost per can of grape juice

y----> the cost per can of apple juice

we know that

6x+4y=13.10 -----> equation A

4x+6y=13.10+0.60

4x+6y=13.70 -----> equation B

Solve the system by elimination

Multiply the equation A by -6 both sides

-36x-24y=-78.6 -------> equation C

Multiply the equation B by 4 both sides

16x+24y=54.8 -------> equation D

Adds equation C and equation D

$-36x-24y=-78.6\\16x+24y=54.8\\----------\\-36x+16x=-78.6+54.5\\-20x=-23.8\\x=1.19$

Substitute the value of x in the equation A

6(1.19)+4y=13.10

4y=5.96

y=1.49

therefore

The cost per can of grape juice is $\$1.19$

The cost per can of apple juice is $\$1.49$

Part 2) Solve the system by substitution

Let

x----> the cost per can of grape juice

y----> the cost per can of apple juice

we know that

6x+4y=13.10

4y=-6x+13.10

y=-1.5x+3.275 -----> equation A

4x+6y=13.10+0.60

4x+6y=13.70

6y=-4x+13.70

y=-(4/6)x+13.70/6

y=--0.67x+2.28 -----> equation B

Substitute equation B in equation A and solve for x

-0.67x+2.28=-1.5x+3.275

1.5x-0.67x=3.275-2.28

0.83x=0.995

x=1.19

Find the value of y

Substitute the value of x in the equation A

y=-1.5(1.19)+3.275=1.49

therefore

The cost per can of grape juice is $\$1.19$

The cost per can of apple juice is $\$1.49$

Part 3) Solve the system by graphing

we have

y=-1.5x+3.275 -----> equation A

y=-(4/6)x+13.70/6 -----> equation B

Remember that

The solution of the system of equations is equal to the intersection point both lines

The solution is the point (1.19,1.49)

see the attached figure

therefore

The cost per can of grape juice is $\$1.19$

The cost per can of apple juice is $\$1.49$

Jennifer's bill for 6 cans of grape juice and 4 cans of apple juice was $13.10. when she got home sh

answered: Guest

a) $ 9.50

b) 17

c) y-intercept (0, 12). this is the initial amount of money that joe had prior to playing any game.

d) x-intercept ( 24, 0). this is the number of games that joe will play before he depletes the initial amount of money that he had.

e) slope is -0.5. joe's balance will reduce by 0.5 for every game that he plays.

domain; [0,24]

range; [0,12]

g) x + 2y = 24

step-by-step explanation:

if joe plays 5 games, this will imply that x = 5. substitute x = 5 in the equation and solve for y;

y = -.50x + 12

y = -0.50(5) + 12

y = 9.50

if joe leaves the arcade with $3.50, this will mean that y = 3.50. plug in y = 3.50 in the given equation and solve for x;

y = -.50x + 12

3.50 = -0.50x + 12

0.50x = 12 - 3.50

0.5x = 8.5

x = 17

the function given is y = -.50x + 12.

the y-intercept is the point where the graph of this function will intersect the y-axis. at this point, the value of x is usually 0. plug in x = 0 in the given equation and determine y;

y = -0.50(0) + 12

y = 12

the y-intercept is thus (0, 12). this is the initial amount of money that joe had prior to playing any game.

the x-intercept refers to the point where the graph of a function intersects with the x-axis. at this point, the value of y is 0. substitute y = 0 in the given equation and solve for x;

0 = -.50x + 12

0.5x = 12

x = 24

x-intercept ( 24, 0). this is the number of games that joe will play before he depletes the initial amount of money that he had.

the slope of the given equation is -0.5. the equation has been given in slope-intercept form. thus the slope is simply the coefficient of x.

joe's balance will reduce by 0.5 for every game that he plays. this is the interpretation of the slope.

domain is the set of x values for which the function is real and defined. the domain will thus be; [0,24]. this will restrict the balance to only assume positive values.

on the other hand, the range is the set of y values for which a function is real and defined. the range in our case will be [0,12]. joe can have between $0 and $12 balance.

the standard form of the equation of a straight line is;

ax + by = c

where a, b, and c are integers.

our equation is given as;

y = -.50x + 12

re-writing the equation we have;

0.5x + y = 12

divide all through by 0.5;

x + 2y = 24

answered: Guest

The percent increase is 25%