The problem describes two scenarios. On Monday, Lule bought 5 scones and 2 large coffees for $16.74. On Tuesday, Rachel bought 4 scones and 3 large coffees for $16.15. The goal is to find the cost of one scone and the cost of one large coffee.

1. Problem Description

The problem describes two scenarios. On Monday, Lule bought 5 scones and 2 large coffees for $16.

7

4. On Tuesday, Rachel bought 4 scones and 3 large coffees for $16.

1

5. 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 set up the following system of equations based on the given information:

$5s + 2c = 16.74$ (Monday)

$4s + 3c = 16.15$ (Tuesday)

We can solve this system of equations using substitution or elimination. Let's use elimination.

Multiply the first equation by 3 and the second equation by 2:

$3(5s + 2c) = 3(16.74) \Rightarrow 15s + 6c = 50.22$

$2(4s + 3c) = 2(16.15) \Rightarrow 8s + 6c = 32.30$

Now, subtract the second equation from the first:

$(15s + 6c) - (8s + 6c) = 50.22 - 32.30$

$7s = 17.92$

$s = \frac{17.92}{7} = 2.56$

Now that we have the value of $s$, substitute it back into one of the original equations to find the value of $c$. Let's use the first equation:

$5s + 2c = 16.74$

$5(2.56) + 2c = 16.74$

$12.80 + 2c = 16.74$

$2c = 16.74 - 12.80$

$2c = 3.94$

$c = \frac{3.94}{2} = 1.97$

Therefore, the cost of one scone is $2.56 and the cost of one large coffee is$1.

9

7.

3. Final Answer

The cost of one scone is $2.56 and the cost of one large coffee is$1.97.