Standardized test practice
62. extended response lenora bought several
pounds of cashews and several pounds of
almonds for a party. the cashews cost $8 per
pound, and the almonds cost $6 per pound.
lenora bought a total of 7 pounds and paid
a total of $48. write and solve a system of
equations to determine the pounds of cashews
and the pounds of almonds that lenora
purchased.

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!

your answer is d 2,500

step-by-step explanation:

the simplified form is

step-by-step explanation:

we want to simplify the expression,

let us change the middle bar to a normal division sign to obtain,

we multiply the first fraction by the reciprocal of the second fraction to obtain,

we factor to obtain,

we cancel the common factors to get,

we simplify to get,

the correct answer is b