Answer: the cost of a milkshake is $2.59
Step-by-step explanation:
Let x represent the cost of a banana split.
Let y represent the cost of a milkshake.
At the ice cream shop, one banana split and five milkshakes cost $16.24. This is expressed as
x + 5y = 16.24- - - - - - - - - - - - -1
If three banana splits and two milkshakes cost $15.05. This is expressed as
3x + 2y = 15.05- - - - - - - - - - - - -2
Multiplying equation 1 by 3 and equation 2 by 1, it becomes
3x + 15y = 48.72
3x + 2y = 15.05
Subtracting, it becomes
13y = 33.67
y = 33.67/13
y = 2.59
Substituting y = 2.59 into equation 1, it becomes
x + 5 × 2.59 = 16.24
x + 12.95 = 16.24
x = 16.24 - 12.95
x = 3.29
