Standardized Test Practice
2 answers:
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.
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.
Now, since you know c = 7 - a, you can substitute 7 - a in the other equation in for c.
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!
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