please help me I need to pass

Question

You have one type of nut that sells for $3.10/lb and another type of nut that sells for $5.70/lb. You would like to have 5.2 lbs of a nut mixture that sells for $4.00/lb. How much of each nut will you need to obtain the desired mixture?

Answer 1

Let x=amount of nuts needed that sell for 3.10/lb.

Let y=amount of nuts needed that sell for 5.70/lb.

You need to solve the following 2 equations simultaneously:

x+y= 5.2 lbs.

3.10x+5.70y= $4.00/lb

Change the first equation to get an expression you can use to substitute in for x or y in the second equation:

either x=5.2-y or y=5.2-x, pick one of these & plug it into the second equation: now you have an equation with a single variable (x or y) depending on which one you picked. Now solve for that variable:

For example:

3.1(5.2-y)+5.7y=4.00 *remember to use the order of operations when you solve it*

16.12-3.1y+5.7y=4.00

16.12-2.6y=4.00

12.12=2.6y *I want to work with positive numbers*

12.12/2.6=y

4.66153846=y * round to 2 decimal places*

y=4.66, which is the amount of nuts(in lbs) you need of the nuts that sell for 5.70/lb.

we know x+y=5.2, so if y=4.66, then just substitute 4.66 in the equation and solve for x:

x+4.66=5.2

x=5.2-4.66=.054, which is the amount of nuts you need (in lbs) that sell for 3.10/lb.