Answer:
8x+6y=48
x+y=7
multiply bottom equation by 6:
8x+6y=48
6x+6y=42
subtract equations:
2x=6
divide 6 by 2:
x=3
therefore:
y=4
Hello!
First, set some variables. Say c = # of pounds of cashews, and a = # of pounds of almonds. With these variables, you can set up a system of equations. The two equations we will be using is how much she paid, and how many pounds she bought.
How much she paid: 8c + 6a = 48
This one can be explained by c being the number of pounds of cashews, therefore multiplying it by 8 would be the amount she paid for Cashews, and the same for the almonds.
How many pounds she bought: c + a = 7
This one is fairly simple. She bought 7 pounds total, and then c + a should therefore equal the total number of pounds she bought, so c + a = 7.
Now, set up the system.
[tex]\left \{ {{8c + 6a = 48} \atop {c + a = 7}} \right.[/tex]
I'm going to be using the method of substitution. That's where you solve for one of the variables in one of the equations, and then substitute that into the other equation.
[tex]\left \{ {{8c + 6a = 48} \atop {c + a = 7}} \right.[/tex]
[tex]\left \{ {{8c + 6a = 48} \atop {c = 7 - a}} \right.[/tex]
Now, since you know c = 7 - a, you can substitute 7 - a in the other equation in for c.
[tex]\left \{ {{8c + 6a = 48} \atop {c = 7 - a}} \right.[/tex]
8 (7 - a) + 6a = 48
And now solve.
8 (7 - a) + 6a = 48
56 - 8a + 6a = 48
-2a = -8
a = 4
To get the other variable, substitute a = 4 into one of the original equations.
c + a = 7
c + 4 = 7
c = 3
Therefore, a = 4 and c = 3. This means that Lenora purchased 4 pounds of almonds and 3 pounds of cashews.
Hope this helped!
