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Sam bought 15 pies and 7 slices of cake for $55.25. If each pie cost 2/5 as much as a slice of cake, what was the total cost of 1 pie and 2 slices of cake​

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KellyAstro

Answer: $10.20

Step-by-step explanation:

Let's first collect the information from the word problem.

We are told:

  • Bought 15 pies and 7 cake slices
  • Total cost was $55.22.
  • Pies cost [tex]\frac{2}{5}[/tex] as much as a slice of cake

We need to solve for:

  • Total cost of 1 pie and 2 cake slices

1. Create an equation/expression:

To solve the problem, we need to find the price of a pie and cake slice.

Using the information gathered, the equation is:

    [tex]55.25 = 7x+15(\frac{2}{5} x)[/tex]

x = the cost of the slice of cake.

2. Simplify/Solve

[tex]55.25 = 7x+15(\frac{2}{5}x)\\55.25 = 7x+15*\frac{2}{5}*x\\55.25 = 7x+6x\\55.25 = 13x\\4.25 = x[/tex]

  • Great! we have the price of a slice of cake. ($4.25)

Remember that the pie is [tex]\frac{2}{5}[/tex] of a slice of cake, so now find the price of the pies.

Pie = [tex]\frac{2}{5} 4.25[/tex]

Pie = $1.70

  • Awesome! We know a slice of cake costs $4.25 and a slice of pie costs $1.70.

3. Check your work!

Check to make sure the math is done correctly!

[tex]55.25=7(4.25)+15(1.70) \\55.25=29.75+25.50\\55.25=55.25[/tex]

Good! It is verified that our calculations are correct.

4. Solve!

1 pie and 2 cakes cost: [tex]1.70+2(4.25)[/tex]

  • $10.20 is our final answer!

  • Hope this helped!~~ -Astro

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