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
