The problem describes two separate purchases of scones and large coffees. 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 one large coffee.

1. Problem Description

The problem describes two separate purchases of scones and large coffees. On Monday, Luis bought 5 scones and 2 large coffees for $16.

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

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3. The goal is to find the cost of one scone and 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 a system of two linear equations:

$5s + 2c = 16.48$

$4s + 3c = 15.83$

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:

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

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

This gives us:

$15s + 6c = 49.44$

$8s + 6c = 31.66$

Now subtract the second equation from the first equation:

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

$15s - 8s + 6c - 6c = 17.78$

$7s = 17.78$

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

So, the cost of one scone is $2.

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4. Now substitute the value of $s$ into one of the original equations to find $c$. Let's use the first equation:

$5s + 2c = 16.48$

$5(2.54) + 2c = 16.48$

$12.70 + 2c = 16.48$

$2c = 16.48 - 12.70$

$2c = 3.78$

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

So, the cost of one large coffee is $1.

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3. Final Answer

The cost of one scone is $2.54 and the cost of one large coffee is$1.

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