Sasha and Francisco were selling lemonade for 25 cents per half cup and 50 cent per full cup. At the end of the day they had collected 15 dollars and had used 37 cups. How many full cup and how many half cups did they sell?
Solution
Let x be the number of full cup sold
Let y be the number of half cup sold
Whether the cup was full or not, they used 37 cups.
Therefore,
x + y = 37
How much money did they make selling half cup lemonade?
They made y × 0.25
How much money did they make selling full cup lemonade?
They made x × 0.50
Money made selling full cup + money made selling half cup = 15
x × 0.50 + y × 0.25 = 17
You end up with a system of linear equation to solve
x + y = 37
x × 0.50 + y × 0.25 = 17
x + y = 37 equation 1
0.50x + 0.25y = 17 equation 2
Solve for y in equation 1
x + y = 37
x - x + y = 37 - x
y = 37 - x
Replace y in equation 2
0.50x + 0.25 (37 - x) = 17
0.50x + 0.25 × 37 - 0.25x = 17
0.50x + 9.25 - 0.25x = 17
0.25x + 9.25 = 17
0.25x + 9.25 - 9.25 = 17 - 9.25
0.25x = 17 - 9.25
0.25x = 7.75
Divide both sides by 0.25
0.25x/0.25 = 7.75/0.25
x = 31
y = 37 - x = 37 - 31 = 6
Sasha and Francisco sold 31 full cup and 6 halh cup of lemonade.
It seems like people love their lemonade
May 21, 18 09:24 AM
Explore exponential and logarithmic functions with these easy to follow math lessons
New math lessons
Your email is safe with us. We will only use it to inform you about new math lessons.
May 21, 18 09:24 AM
Explore exponential and logarithmic functions with these easy to follow math lessons
Our Top Pages
Formula for percentage
Compatible numbers
Basic math test
Basic math formulas
Types of angles
Math problem solver
Algebra word problems
Surface area of a cube
Finding the average
Scale drawings
Everything you need to prepare for an important exam!
K-12 tests, GED math test, basic math tests, geometry tests, algebra tests.
Real Life Math Skills
Learn about investing money, budgeting your money, paying taxes, mortgage loans, and even the math involved in playing baseball.