Answer: A scone costs $2.64, and a large coffee costs $1.92.

Explanation: We can write both scenarios as equations, and write it as a system of equations.

“Luis picked up seven scones and four large coffees. He paid $26.16.”

Let’s express the cost of a scone as x.
Let’s express the cost of a large coffee as y.

The first equation would be 7x + 4y = 26.16.

“Rachel picked up six scones and five large coffees. She paid $25.44.”

Let’s express the cost of a scone as x.
Let’s express the cost of a large coffee as y.

The second equation would be 6x + 5y = 25.44.

The systems of equations is:

7x + 4y = 26.16
6x + 5y = 25.44

Let’s take the first equation and solve for x.

7x + 4y = 26.16
7x = 26.16 - 4y
x = (26.16 - 4y)/7

Let’s substitute x in the second equation for (26.16 - 4y)/7, and solve for y.

6((26.16 - 4y)/7) + 5y = 25.44

Distribute the 6 across 26.16 - 4y in the term 6((26.16 - 4y)/7).

(156.96 - 24y)/7 + 5y = 25.44

Rewrite 5y as 35y/7 so it has a common denominator with (156.96 - 24y)/7.

(156.96 - 24y)/7 + 35y/7 = 25.44

Combine like terms.

(156.96 + 11y)/7 = 25.44

Multiply both sides by 7.

156.96 + 11y = 178.08

Subtract 156.96 from both sides.

11y = 21.12

Divide both sides by 11.

y = 1.92

Substitute y into the first equation.

7x + 4(1.92) = 26.16

Simplify 4(1.92).

7x + 7.68 = 26.16

Subtract 7.68 from both sides.

7x = 18.48

Divide both sides by 7.

x = 2.64

Since x = 2.64, we know that the cost of a scone is $2.64.
Since y = 1.92, we know that the cost of a large coffee is $1.92.

Therefore, a scone costs $2.64, and a large coffee costs $1.92.

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3 years ago