Question

Tim and Elizabeth went to a store.tim bought five pieces of cinnamon rolls and three pieces of muffins for a total of $22 and 90 cents.Elizabeth bought two pieces of cinnamon rolls and ten pieces of muffins for a total of twenty dollars and sixty cents.how much is one piece of cinnamon roll?

Answer 1

Given:

a.) Tim bought five pieces of cinnamon rolls and three pieces of muffins for a total of $22 and 90 cents.

b.) Elizabeth bought two pieces of cinnamon rolls and ten pieces of muffins for a total of twenty dollars and sixty cents.

Let's generate equations based on the given scenarios:

Let,

x = price of each cinnamon roll

y = price of each muffin

a.) Tim bought five pieces of cinnamon rolls and three pieces of muffins for a total of $22 and 90 cents.

`\text{ 5x + 3y = 22.90}`

b.) Elizabeth bought two pieces of cinnamon rolls and ten pieces of muffins for a total of twenty dollars and sixty cents.

`\text{ 2x + 10y = 20.60}`

Using the Substitution Method let's determine the value of x and y.

2x + 10y = 20.60

2x = 20.60 - 10y

2x/2 = (20.60 - 10y)/2

x = 10.30 - 5y (Substitute to Equation a)

5x + 3y = 22.90

5(10.30 - 5y) + 3y = 22.90

51.5 - 25y + 3y = 22.90

-22y = 22.90 - 51.50

-22y = -28.6

-22y/-22 = -28.6/-22

y = $1.30

Therefore, the price of each muffin is $1.30.

Let's now determine the price of each cinnamon roll, x.

Substitute y = 1.30 in Equation b.

2x + 10y = 20.60

2x + 10(1.3) = 20.60

2x + 13 = 20.60

2x = 20.60 - 13

2x = 7.60

2x/2 = 7.60/2

x = $3.80

Therefore, the price of each cinnamon roll is $3.80.