At the ice cream shoppe ,one banana split and five milkshakes cost $16.24.If three banana splits and two milkshakes cost $15.05,find the cost of a milkshake.

The cost of one banana split = $3.29

The cost of one milkshake is = $2.59

Let the cost of one banana split = x

the cost of one milkshake is = y.

So, according to the question:

x+5y=16.24

3x+2y=15.05

Solving the equations we get: x=3.29 and y=2.59.

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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