A store is having a sale on almonds and jelly beans. For 2 kilograms of almonds and 3 kilograms of jelly beans, the total cost is $11. For 6 kllograms of almonds and 5 kilograms of jelly beans, the total cost is $23. Find the cost for each kilogram of almonds and each kilogram of jelly beans. Find cost for each kilogram of almonds :?
Ans find the cost for each kilogram of jelly beans :?

The cost of each kg of almonds is $1.75

The cost of each kg of jelly beans is $2.5

Step-by-step explanation:

We will use the system of linear equations to solve the question

Assume that the cost of 1 kg of almonds is $x, and the cost of 1 kg of jelly beans is $y

∵ For 2 kilograms of almonds and 3 kilograms of jelly beans,

   the total cost is $11

→ Multiply 2 by x and 3 by y, then equate their sum by 11

∴ 2x + 3y = 11 ⇒ (1)

∵ For 6 kilograms of almonds and 5 kilograms of jelly beans, the

   total cost is $23

→ Multiply 6 by x and 5 by y, then equate their sum by 23

∴ 6x + 5y = 23 ⇒ (2)

Now we need to solve this system of equations to find the values of x and y

→ Multiply equation (1) by -3 to make the coefficient of x in it equals

  the coefficient of x in equation (2) in values and differences in signs

∵ -3(2x) + -3(3y) = -3(11)

∴ -6x + -9y = -33 ⇒ (3)

→ Add equations (2) and (3) to eliminate x

∵ (6x + - 6x) + (5y - 9y) = (23 + -33)

∴ -4y = -10

→ Divide both side by -4 to find the value of y

∵  

∴ y = 2.5

→ Substitute the value of y in equation (1) to find x

∵ 2x + 3(2.5) = 11

∴ 2x + 7.5 = 11

→ Subtract 7.5 from both sides

∵ 2x + 7.5 - 7.5 = 11 - 7.5

∴ 2x = 3.5

→ Divide both sides by 2 to find the value of x

∵

∴ x = 1.75

∵ x represents the cost of 1 kg of almonds

∴ The cost of each kg of almonds is $1.75

∵ y represents the cost of 1 kg of jelly beans

∴ The cost of each kg of jelly beans is $2.5