Word problem: John is making lemonade for a party....

[Stine]

John is making lemonade for a party. He has 6 cups of a 40% lemon juice drink. He plans to combine it with a 100% real lemon juice so he can end up with a 60% lemonade drink for the children. How much of the pure (100%) real lemon juice should he add? Write two equations for the situtation and solve system of linear equations.

Uuummm here is a start...

Let x = 40% (.40) lemon juice drink
Let y = 100% (1.0) pure lemon juice

.40x + 1.y = .60x

Can someone help me with getting thsi set up correctly?

Thank you

 

[soroban]

Re: Word problem

Hello, Stine!

John is making lemonade for a party.
He has 6 cups of a 40% lemon juice drink.
He plans to combine it with a 100% real lemon juice
so he can end up with a 60% lemonade drink for the children.
How much of the pure (100%) real lemon juice should he add?
Write two equations for the situtation and solve the system of equations.

It is very tricky to write two equations for this problem.
. . I would solve it with one variable and one equation.

Let \(\displaystyle x\) = amount of pure lemon juice to be added.

He has 6 cups of 40% drink.
. . This contains: \(\displaystyle \:0.40\,\times\,6\:=\:2.4\) cups of lemon juice.

He adds \(\displaystyle x\) cups of 100% juice.
. . This contains: \(\displaystyle \,1.00\,\times\,x\:=\:x\) cups of lemon juice.

Hence, the mixture contains: \(\displaystyle x\,+\,2.4\) cups of lemon juice. [1]


But the mixture is \(\displaystyle x\,+\,6\) cups which contains 60% lemon juice.
. . It contains: \(\displaystyle \,0.6(x\,+\,6)\) cups of lemon juice. [2]


There is our equation: equate [1] and [2].

. . \(\displaystyle \L x\,+\,2.4 \:=\:0.6(x\,+\,6)\)