Linear Diophantine Equations

In a certain basketball game, you can only make 2 point shots and 3 point shots. If you scored exactly 20 points, how many of the following scenarios are possible?

Your answer seems reasonable. Find out if you're right!

You must be logged in to see worked solutions.

That seems reasonable. Find out if you're right!

or

Already have an account? Log in here.

Consider all ordered pairs of integers $(x,y)$ such that \[\frac{5}{x}+\frac{7}{y} = \frac{12}{xy}.\]

The smallest positive integer value of $x$ in these ordered pairs is $1,$ since $x=y=1$ satisfies the equation. What is the second smallest positive integer value of $x$ in these ordered pairs?

\[2\] \[3\] \[4\] \[5\] \[6\] \[7\] \[8\] \[9\]

Your answer seems reasonable. Find out if you're right!

You must be logged in to see worked solutions.

That seems reasonable. Find out if you're right!

or

Already have an account? Log in here.

Jimmy has the high score, 920, in his favorite video game. For each win, he gets 50 points, but for each loss, he loses 36 points. What is the minimum number of games that Jimmy could have played?

Your answer seems reasonable. Find out if you're right!

You must be logged in to see worked solutions.

That seems reasonable. Find out if you're right!

or

Already have an account? Log in here.

If you have infinite pennies ($0.01), nickels ($0.05), and dimes ($0.10), in how many different ways can you make change for $1.00?

Hint: Don't try to list all of the possibilities!

Your answer seems reasonable. Find out if you're right!

You must be logged in to see worked solutions.

That seems reasonable. Find out if you're right!

or

Already have an account? Log in here.

Gummy bears come in packs of 6 and 9. Is there a combination of these packs which gives a total of exactly 100 gummy bears?

Your answer seems reasonable. Find out if you're right!

You must be logged in to see worked solutions.

That seems reasonable. Find out if you're right!

or

Already have an account? Log in here.

Concept Quizzes

Challenge Quizzes

One Equation

Waste less time on Facebook — follow Brilliant.