The problem describes two purchases: - On Monday, Luis bought 5 scones and 2 large coffees for $16.48. - On Tuesday, Rachel bought 4 scones and 3 large coffees for $15.83. The goal is to find the cost of one scone and the cost of one large coffee.

1. Problem Description

The problem describes two purchases:

- On Monday, Luis bought 5 scones and 2 large coffees for $16.

4

8. - On Tuesday, Rachel bought 4 scones and 3 large coffees for $15.

8

3.

The goal is to find the cost of one scone and the cost of one large coffee.

2. Solution Steps

Let $s$ be the cost of one scone and $c$ be the cost of one large coffee.

We can write two equations based on the given information:

$5s + 2c = 16.48$ (Monday)

$4s + 3c = 15.83$ (Tuesday)

We can solve this system of equations. Multiply the first equation by 3 and the second equation by 2 to eliminate $c$:

$3(5s + 2c) = 3(16.48)$

$15s + 6c = 49.44$

$2(4s + 3c) = 2(15.83)$

$8s + 6c = 31.66$

Subtract the second new equation from the first new equation:

$(15s + 6c) - (8s + 6c) = 49.44 - 31.66$

$7s = 17.78$

$s = \frac{17.78}{7} = 2.54$

Now, substitute the value of $s$ into one of the original equations to solve for $c$. We'll use the first equation:

$5(2.54) + 2c = 16.48$

$12.70 + 2c = 16.48$

$2c = 16.48 - 12.70$

$2c = 3.78$

$c = \frac{3.78}{2} = 1.89$

3. Final Answer

The cost of one scone is $2.54 and the cost of one large coffee is$1.89.