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.
