Question

A metal worker has several 1-kilogram bars of a metal alloy that contain 34% copper and several 1-kilogram bars that contain 74% copper. How many bars of each type of alloy should be melted and combined to create 40 kilograms of a 48% copper alloy? Set up and solve a system of equations to find the answer.

Answer 1

The weight of copper in the 48% alloy is 40 * .48 = 19.2 kg
Let x be the weight of copper required in the bars of 34% alloy, and let y be the weight of copper required in the bars of 74% alloy.
x + y = 19.2 ...........(1)
\[\frac{x}{0.34}+\frac{y}{0.74}=40\ ..........(2)\]
Using these two equations, (1) and (2), the answer can be found.

Answer 2

According to question:
Let x is the number of 34% alloy bars taken
and y is the number of 74% copper alloy bars taken
x+y=40..............(i)
and also we have
0.34x+0.74y=0.48(x+y)
this implies
0.34x+0.74y=0.48*40..............(ii)

Answer 3

From equation (1) we can find y in terms of x as follows:
y = 19.2 - x ...........(3)
If you plug the value of y in (3) into equation (2) you can solve for x.

Answer 4

multiplying 1st equation by 0.34 we get
0.34x+0.34y=0.34*40...........(i)
0.34x+0.74y=0.48*40..........(ii)
now (ii)-(i)

Answer 5

i think x and y are identities of 1 kg each.
they can not be broken into pieces
so x+y=40 instead of x+y=19.2 @kropot72

Answer 6

@neer2890 My method leads to the correct solution. The weights of copper are converted to bars later.

Answer 7

so we can say that 26 bars of 34% alloy and 14 bars of 74% alloy are taken to form 48% copper alloy.

Answer 8

let us see @kropot72

Answer 9

Seeing it that way makes a lot more sense thank you!

Answer 10

you're welcome...:)

Answer 11

\[\frac{x}{0.34}+\frac{19.2-x}{0.74}=40\]
which simplifies to
\[1.59x=14.054\]
x = 8.839 kg of copper in 34% alloy.
Weight of 34% alloy = 8.839/0.34=26 kg (or 26 bars weighing 1 kg each)

Answer 12

you can even justify your answer that it's correct.
48% of 40= 19.2 kg
let us see
we have taken 26 bars of 34% alloy
so total quantity of alloy in 26 bars=0.34*26=8.84 kg
and also we have taken 14 bars of 74% alloy
so total quantity of alloy in 14 bars=0.74*14=10.36 kg
so total weight of alloy in 40 kg =(10.36+8.84)=19.2 kg which is 48% of 40 kg

Answer 13

My method does not assume that the answer will be in whole bars.

Answer 14

Thanks @kropot72 that was also helpful!

Answer 15

you're welcome :)

Answer 16

yeah.. it's another way of solving.. thanks @kropot72

Answer 17

will you guys help with another?

Answer 18

please post as a new question.

Answer 19

Jeremy bought x pounds of peanuts for $4.50 per pound and y pounds of cashews for $7.05 per pound at the store for a retirement party. The total bill was $43.65 for 8 pounds of nuts.
Part A Write a system of two equations that could be used to find the number of pounds of peanuts and the number of pounds of cashews bought.
Part B Solve the system. How many pounds of each nut did Jeremy buy?

Answer 20

sure...:)

Answer 21

total bill was for eight pounds
so x+y=8.....(i)
also,
4.5x+7.05y=43.65......(ii)
solve these two equations to find x and y.