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?



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

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

5x + 4(22) = 413

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