SOLUTION: I have a 70% meat and30% meat need to get 37% but it has to weigh 3060pounds

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

Answer by josmiceli(19441)   (Show Source): 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
Answer by Theo(13342)   (Show Source): You can put this solution on YOUR website!
x = pounds of 70% meat
y = pounds of 30% meat.
you want 3060 pounds of 37% meat.

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.

.

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