A local grocery store makes a 6-pound mixture of trail mix. The trail mix contains raisins, sunflower seeds, and chocolate-covered peanuts. The raisins cost $3 per pound, the sunflower seeds cost $1 per pound, and the chocolate-covered peanuts cost $1.50 per pound. The mixture calls for twice as many raisins as sunflower seeds. The total cost of the mixture is $11.50. Write a system of equations for the situation and solve for the amount of each item in the trail mix.

The mass of sunflower seeds in the mixture is 1-pound

The mass of chocolate-covered peanuts in the mixture is 3-pounds

The mass of raisins in the mixture is 2-pounds

Step-by-step explanation:

The given parameters are;

The cost per pound of raisins = $3

The cost per pound of sunflower seeds = $1

The cost per pound of chocolate-covered peanuts = $1.50

The mass of raisings in the mixture = 2 × The mass of sunflower seeds in the mixture

The total cost of the mixture = $11.50

The mass of the mixture = 6-pounds

Let x represent the mass of sunflower seeds in the mixture, and y represents the mass of chocolate-covered peanuts in the mixture, we have;

The mass of raisins in the mixture = 2 × x

The system of equation are;

2·x + x + y = 6...(1)

2·x × 3 + x × 1 + y × 1.5 = 11.50...(2)

Simplifying the above two equations give;

For equation (1), we have;

3·x + y = 6...(1)

For equation (2), we have;

7·x + 1.5·y = 11.50...(2)

Making y the subject of both formulas, gives;

For equation (1), we have;

y = 6 - 3·x

For equation (2), we have;

y = 11.50/1.5 - 7/1.5·x

Equating both equations of y, to find the common solution as follows;

6 - 3·x = 11.50/1.5 - 7/1.5·x

7/1.5·x  - 3·x = 11.50/1.5 - 6

14/3·x  - 3·x = 23/3 - 6

5/3·x = 5/3

x = 3/5 × 5/3 = 1

x = 1

The mass of sunflower seeds in the mixture = x = 1-pound

y = 6 - 3·x =  6 - 3 × 1 = 3

y = 3

-The mass of chocolate-covered peanuts in the mixture = y = 3-pounds

The mass of raisins in the mixture = 2 × x = 2 × 1 = 2-pounds.

answer:

payment just for service  

→

$

87.12

payment for service including tax

→

$

94.09

explanation:

service only with 20% tip  

→

$

72.6

(

1

+

20

100

)

=

$

87.12

in the opening of the question the word 'service' is associated only with the pretax value.

the closing part of the question asks: how much did she pay for the  

service

−−−−−−  

so technically the answer is  

→

$

72.6

(

1

+

20

100

)

=

$

87.12

however, the intention of the question provider may have been that your answer is to be  

$

87.12

(

1

+

8

100

)

=

$

94.09

to 2 decimal places.

'

payment just for service  

→

$

87.12

payment for service including tax

→

$

94.09

tony b

mar 21, 2017

answer:

trying to explain it another way

explanation:

service charge  

.

→

$

72.60

20% tip  

20

100

×

$

72.60

=

$

14.52

−−−−−−  

←

add

$

87.12

tax  

8

100

×

$

87.12

=

$

6.97

−−−−−  

←

add

$

94.09

related questions