Calculating the Amount of Type B Tea in a €12.65/kg Mixture

[tehmatriks]

Homework Statement

Tea served in a canteen is made from a mixture of two different types of tea, type A and type B. Type A costs €12.15 per kg. Type B costs €12.90 per kg. The mixture costs €12.65 per kg.
If the mixture contains 7kg of type A, how many kilograms of type B does it contain?

Homework Equations

The Attempt at a Solution

all I've written so far is: 12.15 x 7 = €85.05
and i don't even know where I am going with that

 

[Nex Vortex]

This problem requires you to set up a single variable algebra equation. You are on the right track with finding the total cost by multiplying the cost per kg and the mass. Now you have to find the total cost of the others, and make an equation out of it.

Type A's cost is:
12.15 * 7 = 85.05 (which you've already correctly gotten)

Type B's cost is:
12.90 * x (since the mass is what we're looking for, we leave it as a variable)

Total cost is:
12.65 * (7 + x) (The total mass is 7 kg from type A, plus the undetermined type B's mass).

So when you put that together you end up with the following equation:
85.05 + 12.90x = 12.65(7+x)

All that is left to do is to solve for x.

 

[tehmatriks]

thanks man, i got it, here's the results

85.05 + 12.90x = 12.65(7+x)
85.05 + 12.90x = 88.55 + 12.65x
-12.65x + 12.90x = 88.55 - 85.05
0.25x = 3.5
x = 14kg