Respuesta :
Answer:
Cost of each cup of coffee is $1.59.
Cost of each bottle of water is $1.39.
Step-by-step explanation:
Let C be the cost of each cup of coffee and B be the cost of each bottle of water.
We have been given that Jackie purchased 3 bottles of water and 2 cups of coffee for the family. So the cost of 3 bottles of water will be 3B and cost of 2 cups of coffee will be 2C.
As Jackie spent $7.35 on these items, so we can represent this information in an equation as:
[tex]3B+2C=7.35...(1)[/tex]
We are also told that Ryan bought 4 bottles of water and 1 cup of coffee for his family. So the cost of 4 bottles of water will be 4B and cost of 1 cup of coffee will be C.
As Ryan spent $7.15 on these items, so we can represent this information in an equation as:
[tex]4B+C=7.15...(2)[/tex]
To find the cost of one cup of coffee we will solve our system of equations using substitution method.
From equation (2) we will get,
[tex]C=7.15-4B[/tex]
Substituting this value in equation (1) we will get,
[tex]3B+2(7.15-4B)=7.35[/tex]
Upon using distributive property we will get,
[tex]3B+14.30-8B=7.35[/tex]
Let us combine like terms.
[tex]3B-8B+14.30-14.30=7.35-14.30[/tex]
[tex]-5B=-6.95[/tex]
Upon multiplying both sides of our equation by -5 we will get,
[tex]\frac{-5B}{-5}=\frac{-6.95}{-5}[/tex]
[tex]B=1.39[/tex]
Therefore, the cost of one bottle of water is $1.39.
Upon substituting B=1.39 in equation (2) we will get,
[tex]4*1.39+C=7.15[/tex]
[tex]5.56+C=7.15[/tex]
Upon subtracting 5.56 from both sides of our equation we will get,
[tex]5.56-5.56+C=7.15-5.56[/tex]
[tex]C=1.59[/tex]
Therefore, the cost of each coffee is $1.59.
Answer:
Water = $1.39 Each
Coffee = $1.59 Each
Step-by-step explanation:
Lets assume that:
W = Water
C = Coffee
Now we have to take the amount of what both Jackie and Ryan Bought.
Jackie got:
[tex]3W + 2C = $7.35[/tex]
Ryan got:
[tex]4W + 1C = $7.15[/tex]
Now that we have both of their orders, we then can use any of the two equations and find the value of both the water and coffee one at a time.
Let's take Ryans equation and solve for C.
[tex]4W + 1C = $7.15[/tex] (NOTE: Let's remove the symbols first to make it clearer)
[tex]4W + 1C = 7.15[/tex]
We then transpose the 4W to the other side to solve for C.
[tex]1C = 7.15 - 4W[/tex]
[tex]C = 7.15 - 4W[/tex]
Now that have a value temporary value for C, we can then substitute it in Jackie's equation.
[tex]3W + 2C = 7.35[/tex]
[tex]3W + 2(7.15 - 4W) = 7.35[/tex]
We then use the distribution rule.
[tex]3W + 14.30 - 8W = 7.35[/tex]
Now we combine LIKE terms.
[tex]3W - 8W = 7.35 - 14.30[/tex]
[tex]-5W = -6.95[/tex]
Then we divide both sides by -5.
[tex]\frac{-5W}{-5} = \frac{-6.95}{-5}[/tex]
We end up with:
[tex]W = 1.39[/tex]
Now that we have the value of the water, we can then substitute it to find the value of the Coffee.
[tex]3W + 2C = 7.35[/tex]
[tex]2C = 7.35 - 3W[/tex]
[tex]2C = 7.35 - 3(1.39)[/tex]
[tex]2C = 7.35 - 4.17[/tex]
[tex]2C = 3.18[/tex]
[tex]\frac{2C}{2} = \frac{3.18}{2}[/tex]
[tex]C = 1.59[/tex]
