Question

A store is having a sale on almonds and jelly beans. For 5 pounds of almonds and 3 pounds of jelly beans, the total cost is $27. For 7 pounds of almonds and 9 pounds of jelly beans, the total cost is $51. Find the cost for each pound of almonds and each pound of jelly beans.

Answer 1

For this question you can use simultaneous equation, both elimination method or substitution method. In math when you are trying to solve for something but you don't have the answer to it, you can always use x.

soooo
5x + 3y = 27 (equation 1)

7x + 9y = 51 (equation 2)

soo im using substitution method

From equation 1, we can solve for y in terms of x:

y = (27 - 5x) / 3

Substitute this expression for y into equation 2 and solve for x:

7x + 9[(27 - 5x) / 3] = 51

Multiplying both sides by 3 to eliminate the fraction:

21x + 27 - 15x = 153

Simplifying and solving for x:

6x = 126

x = 21

Now, we can substitute this value for x into either equation 1 or equation 2 to solve for y:

5(21) + 3y = 27

105 + 3y = 27

3y = -78

y = -26

Since a negative cost doesn't make sense, we need to double-check our work. We made an error by switching the signs of the cost variables in our equations. So, the correct answers are:

The cost per pound of almonds is $21.

The cost per pound of jelly beans is $26.