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On​ Monday, Luis picked up five scones and four large coffees for the office staff. He paid $20.88. On​ Tuesday, Rachel picked up two scones and seven large coffees for the office staff. She paid $18.18. What is the cost of one​ scone? What is the cost of one large​ coffee?

Answer :

The cost of one scone is $2.72, and the cost of one large coffee is $1.82.

Let's denote:

  • [tex]x[/tex] as the cost of one scone.
  • [tex]y[/tex] as the cost of one large coffee.

From the problem, we have two scenarios:

  1. Monday's Purchase:
    Luis bought 5 scones and 4 large coffees for $20.88.
    We can form the equation:
    [tex]5x + 4y = 20.88[/tex]

  2. Tuesday's Purchase:
    Rachel bought 2 scones and 7 large coffees for $18.18.
    We can form the equation:
    [tex]2x + 7y = 18.18[/tex]

We now have a system of linear equations:
[tex]\begin{cases}
5x + 4y = 20.88 \\
2x + 7y = 18.18
\end{cases}[/tex]

To solve this system, we can use the method of substitution or elimination. Here, we will use the elimination method.

  1. First, we need to eliminate one of the variables. Let's eliminate [tex]x[/tex]. To do this, we need to make the coefficients of [tex]x[/tex] in both equations the same.

Multiply the first equation by 2:
[tex]2(5x + 4y) = 2(20.88)[/tex]
[tex]10x + 8y = 41.76[/tex]

Multiply the second equation by 5:
[tex]5(2x + 7y) = 5(18.18)[/tex]
[tex]10x + 35y = 90.90[/tex]

Now, subtract the first modified equation from the second modified equation:
[tex](10x + 35y) - (10x + 8y) = 90.90 - 41.76[/tex]
[tex]10x + 35y - 10x - 8y = 49.14[/tex]
[tex]27y = 49.14[/tex]
[tex]y = \frac{49.14}{27} \approx 1.82[/tex]

So, the cost of one large coffee ([tex]y[/tex]) is approximately $1.82.

Next, we use [tex]y[/tex]'s value to find the cost of one scone ([tex]x[/tex]). Substitute [tex]y = 1.82[/tex] into the original first equation:

[tex]5x + 4(1.82) = 20.88[/tex]
[tex]5x + 7.28 = 20.88[/tex]
[tex]5x = 20.88 - 7.28[/tex]
[tex]5x = 13.60[/tex]
[tex]x = \frac{13.60}{5} \approx 2.72[/tex]

Thank you for reading the article Onâ Monday Luis picked up five scones and four large coffees for the office staff He paid 20 88 Onâ Tuesday Rachel picked up two. We hope the information provided is useful and helps you understand this topic better. Feel free to explore more helpful content on our website!

Rewritten by : Jeany

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