My question is down below because it is too long but i need help for homework

Question

Jenny's aunt wants to buy a mix of almonds and pecans as a birthday gift for Jenny. She wants to buy 6 pounds of nuts in total and spend $50. If almonds cost $7 per pound and pecans cost $9 per pound, how many pounds of pecans should Jenny's aunt buy?

Answer 1

You can solve this problem by creating two equations with two unknowns and solving the system you make.

Let's use the variable a to represent the NUMBER of pounds of almonds she can buy and use the variable p to represent the NUMBER of pounds of pecans she can buy.

Since she buys a total of 6 pounds for both, we can write the following equation: a + p = 6

Then since each pound of almonds costs $7 and each pound of pecans costs $9 and the total cost for both is $50, we can write the following equation:

7a + 9p = 50

Now we can solve these two equations using elimination as follows:

a + p = 6

7a + 9p = 50

Multiply the first equation by -7 to eliminate the variable a and combine the result with the second equation:

-7a -7p = -42

7a + 9p = 50

2p = 8

p = 4 pounds

She can buy 4 pounds of pecans.

Since a + p = 6, she can buy 2 pounds of almonds.