Thank you for visiting On Monday Luis picked up seven scones and four large coffees He paid 26 16 On Tuesday Rachel picked up six scones and five large. This page is designed to guide you through key points and clear explanations related to the topic at hand. We aim to make your learning experience smooth, insightful, and informative. Dive in and discover the answers you're looking for!
Answer :
Answer: A scone costs $2.64, and a large coffee costs $1.92.
Explanation: We can write both scenarios as equations, and write it as a system of equations.
“Luis picked up seven scones and four large coffees. He paid $26.16.”
Let’s express the cost of a scone as x.
Let’s express the cost of a large coffee as y.
The first equation would be 7x + 4y = 26.16.
“Rachel picked up six scones and five large coffees. She paid $25.44.”
Let’s express the cost of a scone as x.
Let’s express the cost of a large coffee as y.
The second equation would be 6x + 5y = 25.44.
The systems of equations is:
7x + 4y = 26.16
6x + 5y = 25.44
Let’s take the first equation and solve for x.
7x + 4y = 26.16
7x = 26.16 - 4y
x = (26.16 - 4y)/7
Let’s substitute x in the second equation for (26.16 - 4y)/7, and solve for y.
6((26.16 - 4y)/7) + 5y = 25.44
Distribute the 6 across 26.16 - 4y in the term 6((26.16 - 4y)/7).
(156.96 - 24y)/7 + 5y = 25.44
Rewrite 5y as 35y/7 so it has a common denominator with (156.96 - 24y)/7.
(156.96 - 24y)/7 + 35y/7 = 25.44
Combine like terms.
(156.96 + 11y)/7 = 25.44
Multiply both sides by 7.
156.96 + 11y = 178.08
Subtract 156.96 from both sides.
11y = 21.12
Divide both sides by 11.
y = 1.92
Substitute y into the first equation.
7x + 4(1.92) = 26.16
Simplify 4(1.92).
7x + 7.68 = 26.16
Subtract 7.68 from both sides.
7x = 18.48
Divide both sides by 7.
x = 2.64
Since x = 2.64, we know that the cost of a scone is $2.64.
Since y = 1.92, we know that the cost of a large coffee is $1.92.
Therefore, a scone costs $2.64, and a large coffee costs $1.92.
Explanation: We can write both scenarios as equations, and write it as a system of equations.
“Luis picked up seven scones and four large coffees. He paid $26.16.”
Let’s express the cost of a scone as x.
Let’s express the cost of a large coffee as y.
The first equation would be 7x + 4y = 26.16.
“Rachel picked up six scones and five large coffees. She paid $25.44.”
Let’s express the cost of a scone as x.
Let’s express the cost of a large coffee as y.
The second equation would be 6x + 5y = 25.44.
The systems of equations is:
7x + 4y = 26.16
6x + 5y = 25.44
Let’s take the first equation and solve for x.
7x + 4y = 26.16
7x = 26.16 - 4y
x = (26.16 - 4y)/7
Let’s substitute x in the second equation for (26.16 - 4y)/7, and solve for y.
6((26.16 - 4y)/7) + 5y = 25.44
Distribute the 6 across 26.16 - 4y in the term 6((26.16 - 4y)/7).
(156.96 - 24y)/7 + 5y = 25.44
Rewrite 5y as 35y/7 so it has a common denominator with (156.96 - 24y)/7.
(156.96 - 24y)/7 + 35y/7 = 25.44
Combine like terms.
(156.96 + 11y)/7 = 25.44
Multiply both sides by 7.
156.96 + 11y = 178.08
Subtract 156.96 from both sides.
11y = 21.12
Divide both sides by 11.
y = 1.92
Substitute y into the first equation.
7x + 4(1.92) = 26.16
Simplify 4(1.92).
7x + 7.68 = 26.16
Subtract 7.68 from both sides.
7x = 18.48
Divide both sides by 7.
x = 2.64
Since x = 2.64, we know that the cost of a scone is $2.64.
Since y = 1.92, we know that the cost of a large coffee is $1.92.
Therefore, a scone costs $2.64, and a large coffee costs $1.92.
Thank you for reading the article On Monday Luis picked up seven scones and four large coffees He paid 26 16 On Tuesday Rachel picked up six scones and five large. We hope the information provided is useful and helps you understand this topic better. Feel free to explore more helpful content on our website!
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Rewritten by : Jeany
The costs of scone $2.64, and a large coffee costs $1.92.
What is a system of equations?
A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.
We can write both scenarios as equations;
Let’s the cost of a scone as x.
Let’s the cost of a large coffee as y.
The first equation ;
7x + 4y = 26.16.
Also,
Let’s the cost of a scone as x.
Let’s the cost of a large coffee as y.
The second equation ;6x + 5y = 25.44.
The systems of equations are;
7x + 4y = 26.16
6x + 5y = 25.44
The first equation and solve for x.
7x + 4y = 26.16
7x = 26.16 - 4y
x = (26.16 - 4y)/7
Now substitute x in the second equation for (26.16 - 4y)/7, and solve for y.
6((26.16 - 4y)/7) + 5y = 25.44
Distribute the 6 across 26.16 - 4y in the term 6((26.16 - 4y)/7).
(156.96 - 24y)/7 + 5y = 25.44
(156.96 - 24y)/7 + 35y/7 = 25.44
Combine like terms;
(156.96 + 11y)/7 = 25.44
Multiply both sides by 7;
156.96 + 11y = 178.08
Then Subtract 156.96 from both sides;
11y = 21.12
y = 1.92
Substitute y into the first equation;
7x + 4(1.92) = 26.16
7x + 7.68 = 26.16
7x = 18.48
x = 2.64
Since x = 2.64, the cost of a scone is $2.64.
Since y = 1.92, the cost of a large coffee is $1.92.
Hence, scone costs $2.64, and a large coffee costs $1.92.
Learn more about equations here;
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