Question

One 8.3 ounce can of Red Bull contains energy in two forms: 27 grams of sugar and 80 milligrams of caffeine. One 23.5 ounce can of Jolt Cola contains 94 grams of sugar and 280 milligrams of caffeine. In Exercises 41–44, determine the number of cans of each drink that when combined will contain the specified nerve- jangling combination of sugar and caffeine. 41. 148 grams sugar, 440 milligrams caffeine. 42. 309 grams sugar, 920 milligrams caffeine. 43. 242 grams sugar, 720 milligrams caffeine. 44. 457 grams sugar, 1360 milligrams caffeine.x
Determine the number of cans of each drink that when combined will contain 403 grams sugar and 1200 milligrams caffeine.

Answer 1

Answer:

41)  2 Red Bull and 1 Jolt Cola

42) 1 Red Bull and 3 Jolt Cola

43) 2 Red Bull and 2 Jolt Cola

44) 3 Red Bull and 4 Jolt Cola

Determine the number of cans of each drink that when combined will contain 403 grams sugar and 1200 milligrams caffeine: 1 Red Bull and 4 Jolt Cola

Step-by-step explanation:

Let X be the cans of Red Bull.

Let Y be the cans of Jolt Cola.

41)

One can of Red Bull has 27g of sugar. One can of Jolt cola has 94g of sugar. So we have the equation:

X(27)+Y(94)=148...(1)

One can of Red Bull has 80mg of caffeine. One can of Jolt cola has 280mg of caffeine. So we have the equation:

X(80)+Y(280)=440...(2)

We find the answear by solving the system of equations:

27X+94Y=148...(1)

80X+280Y=440...(2)

Solving the system:

27X+94Y=148...(1)

27X=148-94Y

X=148/27 -(94/27)Y

Substituting X in (2)

80X+280Y=440...(2)

80[148/27 -(94/27)Y]+280Y=440

(11840/27)-(7520/27)Y+280Y=440

(11840/27)+(40/27)Y=440

(40/27)Y=440-(11840/27)

(40/27)Y=40/27

Y=1

Substituting Y in (1)

27X+94Y=148...(1)

27X+94(1)=148

27X+94=148

27X=148-94

X=54/27

X=2

So we need 2 cans of Red Bull and 1 of Jolt Cola to get 148g of sugar and 440mg of caffeine.

42) Following the same steps we have:

27X+94Y=309...(1)

80X+280Y=920...(2)

Solving the system:

27X+94Y=309...(1)

27X=309-94Y

X=309/27 -(94/27)Y

Substituting X in (2)

80X+280Y=920...(2)

80[309/27 -(94/27)Y]+280Y=920

(24720/27)-(7520/27)Y+280Y=920

(24720/27)+(40/27)Y=920

(40/27)Y=920-(24720/27)

(40/27)Y=40/9

Y=3

Substituting Y in (1)

27X+94Y=309...(1)

27X+94(3)=309

27X+282=309

27X=27

X=1

So we need 1 can of Red Bull and 3 of Jolt Cola to get 309g of sugar and 920mg of caffeine.

43) Following the same steps we have:

27X+94Y=242...(1)

80X+280Y=720...(2)

Solving the system:

27X+94Y=242...(1)

27X=242-94Y

X=242/27 -(94/27)Y

Substituting X in (2)

80X+280Y=720...(2)

80[242/27 -(94/27)Y]+280Y=720

(19360/27)-(7520/27)Y+280Y=720

(19360/27)+(40/27)Y=720

(40/27)Y=720-(19360/27)

(40/27)Y=80/27

Y=2

Substituting Y in (1)

27X+94(2)=242...(1)

27X+188=242

27X=54

X=2

So we need 2 can of Red Bull and 2 of Jolt Cola to get 242g of sugar and 720mg of caffeine.

43) Following the same steps we have:

27X+94Y=457...(1)

80X+280Y=1360...(2)

Solving the system:

27X+94Y=457...(1)

27X=457-94Y

X=457/27 -(94/27)Y

Substituting X in (2)

80X+280Y=1360...(2)

80[457/27 -(94/27)Y]+280Y=1360

(36560/27)-(7520/27)Y+280Y=1360

(36560/27)+(40/27)Y=1360

(40/27)Y=1360-36560/27

(40/27)Y=160/27

Y=4

Substituting Y in (1)

27X+94Y=457...(1)

27X+94(4)=457

27X+376=457

X=3

So we need 3 cans of Red Bull and 4 of Jolt Cola to get 457g of sugar and 1360mg of caffeine.

Determine the number of cans of each drink that when combined will contain 403 grams sugar and 1200 milligrams caffeine

Following the same steps we have:

27X+94Y=403...(1)

80X+280Y=1200...(2)

Solving the system:

27X+94Y=403...(1)

27X=403-94Y

X=403/27 -(94/27)Y

Substituting X in (2)

80X+280Y=1200...(2)

80[403/27 -(94/27)Y]+280Y=1200

(32240/27)-(7520/27)Y+280Y=1200

(32240/27)+(40/27)Y=1200

(40/27)Y=1200-(32240/27)

(40/27)Y=160/27

Y=4

Substituting Y in (1)

27X+94Y=403...(1)

27X+94(4)=403

27X=-94(4)+403

X=1

So we need 1 can of Red Bull and 4 of Jolt Cola to get 403g of sugar and 1200mg of caffeine.