Thank you for visiting On Monday Luis picked up five scones and six large coffees for the office staff He paid 23 91 On Tuesday Rachel picked up two. 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:
Step-by-step explanation:
5s + 6c = 23.91
2s + 7c = 17.89
10s + 12c = 47.82
-10s - 35c = -89.45
-23c = -41.63
c = $1.81 for a large coffee
2s + 7(1.81) = 17.89
2s = 5.22
s = $2.61 for a scone
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Rewritten by : Jeany
a) The cost of one scone is $2.61.
b) The cost of one large coffee is $1.81.
Let the cost of scones be s and the cost of coffees be c.
On Monday, Luis picked up five scones and six large coffees for the office staff. He paid $23.91.
So, the equation is [tex]5s+6c=23.91 -------(i)[/tex]
On Tuesday, Rachel picked up two scones and seven large coffees for the office staff. She paid $17.89.
[tex]2s+7c=17.89 -------(ii)[/tex]
Multiply equation (i) by 2, we get [tex]10s+12c=47.82 -------(iii)[/tex]
Multiply equation (ii) by 5, we get [tex]10s+35c=89.45 -------(iv)[/tex]
Subtract equation (iii) from the equation (iv), we get
[tex]10s+35c-(10s+12c)=89.45-47.82[/tex]
[tex]10s+35c-10s-12c=89.45-47.82[/tex]
[tex]23c=41.63[/tex]
[tex]c=\frac{41.63}{23}[/tex]
[tex]c=\$1.81[/tex]
Substitute c=1.81 in equation (ii), we get
[tex]2s+7(1.81)=17.89[/tex]
[tex]2s+12.67=17.89[/tex]
[tex]2s=17.89-12.67[/tex]
[tex]2s=5.22[/tex]
[tex]s=\frac{5.22}{2}[/tex]
[tex]s=\$2.61[/tex]
Therefore,
a) The cost of one scone is $2.61.
b) The cost of one large coffee is $1.81.
To learn more about the linear system of an equations visit:
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