**Problem:**

Algebra-Functions and Equations (**InterMath**)
**A ski resort offers two package plans.**
**Plan A gives one person four nights lodging and
three dinners for $326.**
**Plan B gives one person five nights lodging and
four dinners for $413.**
**Assuming that the costs per night for lodging and
dinner are the same for both plans, **

how much does one dinner cost?

**Solution:**
Plan A 4 nights lodging + 3 dinners = $326

Plan B 5 nights lodging + 4 dinners = $413

x= cost of one nights lodging

y= cost of one dinner
Equation for Plan A

5x +4 y = 413

Equation for Plan B

4x +3y = 326

Solve Equation for Plan A for x: 5x + 4y = 413

x= (413 4y)/5

x= (413/5) (4/5)y
Substitute that value of x into the Equation for Plan
B and solve for y:

4x + 3y = 326

4((413/5) (4/5)y)+ 3y = 326

y=22
To check your work, substitute y into equation for
Plan A and solve for x.

5x + 4(22) = 413

x=65
**The cost of one dinner in both Plan A and Plan B
is y= $22.**

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