Question

Four bagels and five muffins cost $9. Two bagels and ten muffins cost $15. How much does a bagel cost? How much does a muffin cost? Bagel: $[.5] Muffin: $[1.4]

Answer 1

The cost of a bagel is $0.5

The cost of a muffin is $1.4

Step-by-step explanation:

The given is:

• Four bagels and five muffins cost $9
• Two bagels and ten muffins cost $15

We need to find the cost of a bagel and the cost of a muffin

Assume that the cost of a bagel is $x and the cost of a muffin is $y

∵ The cost of one bagel = $x

∵ The cost of one muffin = $y

∵ Four bagels and five muffins cost $9

∴ 4 x + 5 y = 9 ⇒ (1)

∵ Two bagels and ten muffins cost $15

∴ 2 x + 10 y = 15 ⇒ (2)

Now let us solve the system of equations to find the values of x and y

Multiply equation (1) by -2 to eliminate y

∵ -2(4 x) + -2(5 y) = -2(9)

∴ -8 x - 10 y = -18 ⇒ (3)

- Add equations (2) and (3)

∴ -6 x = -3

- Divide both sides by -6

∴ x = 0.5

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

∵ 4(0.5) + 5 y = 9

∴ 2 + 5 y = 9

- Subtract 2 from both sides

∴ 5 y = 7

- Divide both sides by 5

∴ y = 1.4

∵ x represents the cost of a bagel

∵ y represents the cost of a muffin

∴ The cost of a bagel is $0.5

∴ The cost of a muffin is $1.4

The cost of a bagel is $0.5

The cost of a muffin is $1.4

Learn more:

You can learn more about the system of linear equations in brainly.com/question/6075514

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