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The cost of a bagel at Tim Horton’s is $0.99 and the cost of a large coffee is $1.29. If Derek purchases 4 more bagels than large coffees and spends $10.80 total, how many of each did he purchase?

Respuesta :

MrRoyal

Answer:

7 Bagels and 3 Large Coffee

Step-by-step explanation:

Represent Large Coffee with L and Bagel with B.

We have that:

[tex]0.99B + 1.29L = 10.80[/tex] ---- Amount spent

and

[tex]B = L + 4[/tex] ---- Quantity

Required

Determine the value of L and B

Substitute L + 4 for B in the first equation

[tex]0.99B + 1.29L = 10.80[/tex]

[tex]0.99(4 + L) + 1.29L = 10.80[/tex]

Open Bracket

[tex]3.96 + 0.99L + 1.29L = 10.80[/tex]

[tex]3.96 + 2.28L = 10.80[/tex]

Collect Like Terms

[tex]2.28L = 10.80 - 3.96[/tex]

[tex]2.28L = 6.84[/tex]

Solve for L

[tex]L = 6.84/2.28[/tex]

[tex]L = 3[/tex]

Recall that

[tex]B = 4 + L[/tex]

[tex]B = 4 + 3[/tex]

[tex]B = 7[/tex]

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