Linear Inequalities

Linear Inequalities: Level 1 Challenges


Which inequality is represented in the above number line?

The diagram shows how a mobile will be balanced when left to hang.

What are the relative weights of these shapes?

Paula Picasso makes her living by painting. She paints small portraits for $20, large landscapes for $50, and masterpieces for $1000.

Paula's goal is to make at least $2800. She has already sold 1 masterpiece and 23 landscapes. How many portraits must she sell to reach her goal?

You should know that

ab+cda+cb+d. \frac{a}{b} + \frac{c}{d} \ne \frac{a+c}{b+d}.

However, if a,b,c,da, b, c, d are positive integers that satisfy ab<cd,\frac{a}{b} < \frac{c}{d}, what can we say about a+cb+d?\frac{a+c}{b+d} ?

These two numbers are very close together:

1223530.3456,     752170.3456 \large \frac{122}{353} \approx 0.3456, \ \ \ \ \ \frac{75}{217} \approx 0.3456

Which of these numbers is larger?


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