At the fair, you buy 3 sausage sandwiches and a milkshake and it costs you $8.25. Your friend buys 1 sausage sandwich and 2 milkshakes and her total is $5.25. What is the cost of one sandwich and one milkshake?
+4473 Let's make a system of equations:
x = cost of sausage sandwiches and y = cost of milkshakes
(1) 3x + y = 8.25
(2) x + 2y = 5.25
We can solve for x or y in either equation and substitute it to the other.
Let's solve for y in equation(2).
x + 2y = 5.25, subtract x from both sides: 5.25 - x = 2y
Next, solve for y by dividing both sides by 2 = 2.625 - (1/2)x = y.
Now, substitute this - 2.625 - (1/2)x = y into equation(1) for y.
3x + y = 8.25 --> 3x + 2.625 - (1/2)x = 8.25. Now solve for x.
Collect like terms - 3x - (1/2)x = 2.5x and subtract 2.625 from both sides to obtain: 2.5x = 5.625. Divide both sides by 2.5 to obtain x = 2.25 or $2.25 for the cost of one sausage sandwich.
Substitute the value of x = 2.25 into either equation(1) or (2) to solve for y, the price of one milkshake.
3x + y = 8.25 --> 3(2.25) + y = 8.25 --> 6.75 + y = 8.25. Subtract 6.75 from both sides to obtain y = 1.50 or $1.50 for the cost of one milkshake.
Now, do a check to see if the values for x and y make sense.
3x + y = 8.25 --> 3(2.25) + 1.50 ?= 8.25 --> Yes.
x + 2y = 5.25 --> 2.25 + 2(1.50) ?=5.25 --> Yes.
Therefore, the cost of one sausage sandwich is $2.25 and the cost of one milkshake is $1.50.
