This is the solution to the algebra mixture word problem # 7 which read:

"If a merchant has two types of tea, one worth $2.70 per kilogram and the other worth $3.00 per kilogram, how many kilograms of each type should the merchant use in order to produce 30 kilograms of a blend that is worth $2.95 per kilogram?"

Even though this involves money we treat it like a mixture problem.

You got to unknowns but if you look at it as having x = 1 amount and y = 30 -x then you just have x, and 30 -x so...

Its the x amount * the 270 cent worth tea plus the 30 - x amount * the 300 cent worth tea is going to equal 30 * 295 cent blend

270 * x + 300(30-x) = 30(295)

270x + 9000 - 300x = 8850

-30x = -150

30x = 150

x = 150/30 = 5

so 5 kilograms of the 270 cent or $2.70 tea and 30 -5 or 25 kilograms of the 300 cent or $3.00 tea would need to be mixed together to make 30 kilograms of the $2.95 cent tea.

check 270 * 5 + 300 * 25 = 30*295

1350 + 7500 = 8850

8850 = 8850

## Wednesday, October 7, 2009

### Mixture Problem # 6 Solution

### Number Problem 7 Solution

This is the solution to the algebra number word problem 7 which asked "If the Numerator and Denominator of a certain fraction are both increased by 3, the resulting fraction equals 2/3. If the Numerator and Denominator are both decreased by 2, the resulting fraction equals 1/2. Determine the fraction."

Ok so you have 2 unknowns --> x the numerator and y the denominator. You can solve 2 unknowns with 2 equations. They give you 2 equations.

(x+3)/(y+3) = 2/3 and

(x-2)/(y-2) = 1/2

take the (x+3)/(y+3) = 2/3 and cross multiply and get:

2(y+3) = 3(x+3) which is

2y + 6 = 3x + 9

Now take the second equation: (x-2)/(y-2) = 1/2 and cross multiply

2(x-2) = 1(y-2) which makes

2x - 4 = y - 2 now solve for y

y = 2x - 2

ok now plug this back into the 1st equation for y which we broke down to :

2y + 6 = 3x + 9 so you get 2(2x-2) + 6 = 3x + 9 solve for x

4x - 4 + 6 = 3x+ 9

x= 7 ok now plug 7 into y = 2x - 2 and get y = 2(7) -2 = 12

so the numerator is 7 and the denominator is 12 = 7/12

to check add 3 to the top and bottom and get 10/15 = 2/3

and subtract 2 from the top and bottom and get 5/10 = 1/2