Question 508940: I have a 70% meat and30% meat need to get 37% but it has to weigh 3060pounds Found 3 solutions by mananth, josmiceli, Theo:Answer by mananth(16946) (Show Source):
You can put this solution on YOUR website! ---------price ---------price ---------------- quantity
Meat type I 70 ---------------- x pounds
Meat type II 30 ---------------- 3060 - x pounds
Mixture 37.00% ---------------- 3060
70 x + 30 ( 3060 - x ) = 37 * 3060
70 x + 91800 - 30x= 113220
70 x - 30 x= 113220 - 91800
40 x = 21420
/ 40
x = 535.5 pounds 70.00% Meat type I
2524.5 pounds 30.00% Meat type II
You can put this solution on YOUR website! Let = pounds of 70% meat needed
Let = pounds of 30% meat needed
given:
(1) pounds
(2)
--------------------------
(2)
(2)
Multiply both sides of (1) by
and subtract (1) from (2)
(2)
(1)
and, since
(1)
(1)
(1)
535.5 pounds of 70% meat are needed
2524.5 pounds of 30% meat are needed
check answer:
(2)
(2)
(2)
(2)
(2)
OK
first equation is:
.7x + .3y = .37*3060
simplify to get:
.7x + .3y = 1132.2
second equation is:
x + y = 3060
solve these equation simultaneously to get your answer.
multiply both sides of the second equation by .7 to get:
.7x + .7y = .7*3060 which becomes:
.7x + .7y = 2142 (third equation)
subtract first equation from third equation to get:
.7x + .7y = 2142 minus:
.7x + .3y = 1132.2 becomes:
.4y = 1009.8
divide both sides of this equation by .4 to get:
y = 1009.8/.4 = 2524.5
since x + y = 3060, this means that x = 3060 - 2524.5 = 535.5
we have:
x = 535.5
y = 1009.8
original equation is:
.7x + .3y = .37*3060
substitute 535.5 for x and 2524.5 for y to get:
.7*535.5 + .3*2524.5 = .37*3060
simplify this to get:
374.85 + 757.35 = 1132.2
simplify this further to get:
1132.2 = 1132.2
values of 535.5 for x and 2524.5 for y are confirmed as good.
these are the answer to the question.
you need 535.5 pounds of 70% meat and 2524.5 pounds of 30% meat to make 3060 pounds of 37% meat.
