Question 1186459: How much coffee costing P40 per kilo must be added to 150 kilos costing P48 per kilo to make a mixture costing P45 per kilo? Found 3 solutions by ikleyn, josgarithmetic, greenestamps:Answer by ikleyn(52798) (Show Source):
You can put this solution on YOUR website! .
How much coffee costing P40 per kilo must be added to 150 kilos costing P48 per kilo to make a mixture costing P45 per kilo?
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x = kilograms to add.
Money equation
40*x + 48*150 = 45*(150+x)
From the equation
40x + 48*150 = 45*150 + 45x
48*150 - 45*150 = 45x - 40x
(48 - 45)*150 = 5x
3*150 = 5x
x = = 3*30 = 90.
ANSWER. 90 kilograms to add.
CHECK. Ingredients cost 40*90 + 48*150 = 10800.
Mixture cost 45*(150+90) = 10800, the same amount of money. ! Correct !
You can put this solution on YOUR website! ------------------------------------------------------------------------------------------------------------------------------
How much coffee costing P40 per kilo must be added to 150 kilos costing P48 per kilo to make a mixture costing P45 per kilo?
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How much coffee costing L per kilo must be added to V kilos costing H per kilogram to make a mix costing T per kilogram?
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u, amount of coffee priced at L to add
u+V, amount of mixture in kilograms
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L = P40 per kilo
H = P48 per kilo
V = 150 kilos
T = P45 per kilo
If you like to solve problems by plugging numbers into a formula without any understanding of HOW the problem is being solved, use the method shown by tutor @josgarithmetic.
If you want to solve the problem using a formal algebraic method that is easy to understand, use the method shown by tutor @ikleyn.
And if you want to solve any 2-part mixture problem like this quickly without formal algebra, you can try this method:
(1) Picture the three costs per kilo on a number line -- 40, 45, and 48 -- and observe/calculate that 45 is 5/8 of the way from 40 to 48.
(2) That means 5/8 of the mixture is the higher-priced coffee.
So the 150 kilos that you started with is 5/8 of the mixture; that means the 3/8 of the mixture that you added is 90 kilos.
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