Luis bought 5 scones and 2 large coffees for $16.74. Rachel bought 4 scones and 3 large coffees for $16.15. We are given that one scone costs $1.97. We want to find the cost of one large coffee.

1. Problem Description

Luis bought 5 scones and 2 large coffees for $16.

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

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5. We are given that one scone costs $1.

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7. We want to find 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 are given:

$5s + 2c = 16.74$

$4s + 3c = 16.15$

We are also given that $s = 1.97$. Substituting this value into the two equations, we have:

$5(1.97) + 2c = 16.74$

$4(1.97) + 3c = 16.15$

Simplifying the first equation:

$9.85 + 2c = 16.74$

$2c = 16.74 - 9.85$

$2c = 6.89$

$c = \frac{6.89}{2}$

$c = 3.445$

Simplifying the second equation:

$7.88 + 3c = 16.15$

$3c = 16.15 - 7.88$

$3c = 8.27$

$c = \frac{8.27}{3}$

$c = 2.75666...$

We have two different values for $c$, so we need to check the problem statement. We are given that one scone is $1.97$. Substituting this value into the two equations:

Equation 1: $5s + 2c = 16.74$

$5(1.97) + 2c = 16.74$

$9.85 + 2c = 16.74$

$2c = 16.74 - 9.85$

$2c = 6.89$

$c = 6.89/2$

$c = 3.445$

Equation 2: $4s + 3c = 16.15$

$4(1.97) + 3c = 16.15$

$7.88 + 3c = 16.15$

$3c = 16.15 - 7.88$

$3c = 8.27$

$c = 8.27/3$

$c = 2.756666...$

There appears to be an inconsistency in the problem. Let us assume the cost of one scone is not exactly 1.

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7. $5s + 2c = 16.74$

$4s + 3c = 16.15$

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

$15s + 6c = 50.22$

$8s + 6c = 32.30$

Subtract the second equation from the first:

$7s = 17.92$

$s = 17.92/7 = 2.56$

Substitute $s = 2.56$ into the first equation:

$5(2.56) + 2c = 16.74$

$12.8 + 2c = 16.74$

$2c = 16.74 - 12.8$

$2c = 3.94$

$c = 3.94/2 = 1.97$

However, we are given the cost of one scone is $1.97$, not $2.56$. The two given equations and the price of the scone are contradictory. Since we're given the price of the scone is $1.97$, we can solve for the price of the coffee using the first equation.

$5(1.97) + 2c = 16.74$

$9.85 + 2c = 16.74$

$2c = 16.74 - 9.85 = 6.89$

$c = 6.89/2 = 3.445$

3. Final Answer

The cost of one large coffee is $3.

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