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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