algebra
posted by anna on .
A coffee shop sells small cups of coffee and large cups of coffee.
A small cup of coffee costs $2.
A large cup of coffee costs $3.
On Tuesday, the store sold a total of 155 cups of coffee for a total of $335.
How many small cups of coffee did the store sell on Tuesday?

Conventional algebra:
x=number of small cups
y=number of large cups
form the system of equations
x+y=155
2x+3y=335
Solve the system for x and y.
Quick way by substituting directly:
Let 155x=number of large cups
2x+3(155x)=335
Solve the linear equation for x.
Faster way by mental calculations:
Assume all sold are small,
then proceeds
=2x155=310
Money leftover = $335310 = 25
Exchange 25 small cups for 25 large cups for $25, so
small cups = 15525=130
large cups = 25.