I need help on this question dealing with math ASAP.

Question

a store is having a sale on jelly beans and almonds. for 8 pounds of jelly beans and 3 pounds of almonds, the total cost is $21. for 2 pounds of jelly beans and 5 pounds of almonds, the total cost is $18. find the cost for each pound of jelly beans and each pound of almonds.

Answer 1

Let j be the price of jelly beans and a be the price of almonds.

To determine the price of a bag of almonds you multiply the weight in pounds times the price in dollars per pound.

So the following equation is for the first statement:

8j + 3a = 21

And the second statement results in this equation:

2j + 5a = 18

Both of these conditions must be true. To solve these equations there are several methods. An easy way is to use Elimination. To use Elimination, we look for a way to add the two equations together to eliminate one of the variables. We notice that 8j is a multiple of 2j so if we multiply the second equation by -4, the 2j will turn into -8j and when added to the first equation, the j's will be eliminated.

So multiplying the second equation by -4 we get:

-8j - 20a = -72

Placing the first equation above the second and adding we get:

8j + 3a = 21

-8j - 20a = -72

-------------------

-17a = -51

dividing by -17 yields a = 3

Plugging a = 3 into the first equation we get:

8j + 3(3) = 21

or 8j + 9 = 21

or 8j = 12

or j = 1.5

Therefore, the price of almonds is $3.00 per pound and the price of jelly beans is $1.50 per pound

Answer 2

Let's use A for almonds and J for jellybeans.

8J + 3A = 21

2J + 5A = 18

Since you cannot solve a problem with two variables, we have to find a way to get rid of one of the variables. Notice that 2J (in the second equation) can be multiplied by 4 to get 8J (like in the first equation). So, let's multiply everything in the second equation by 4, and then subtract the first equation from the second.

2J(4) + 5A(4) = 18(4)

8J + 20A = 72

8J - 8J = 0; 20A - 3A = 17A; 72 - 21 = 51

Now we have 17A = 51. Divide both sides by 17. A = 3

So a pound of almonds costs $3.

Now that we know that, we can plug 3 into either equation instead of A and solve for J.

8J + 3A = 21.

8J + 9 = 21

8J = 12

J = 1 1/2

Jelly beans cost $1.50 per pound.