Pre-Algebra

Omar has a new debit card. He earns 1,800 reward points for spending 300 dollars. At this rate, if Omar earned 600 reward points, how much money did he spend?

Step-by-step solution with explanation

Final Answer

Omar spent 100$

Step-by-step solution

1

Set up a ratio from given info

We know Omar earns 1,800 points for every $300 spent. We set up a proportion comparing points to dollars to find the unknown spending amount.
2

Cross multiply to solve for x

Cross multiplication means we multiply the top of one fraction by the bottom of the other. This clears the fractions and gives us a simple equation to solve.
3

Simplify the right side

We multiply 600 by 300 to get 180,000. Now we just need to isolate x.
4

Divide both sides by 1800

Dividing both sides by 1,800 gives us x = 100. This tells us how many dollars Omar spent.

Understanding this problem

Learning Insight

This is a unit rate problem. The rate is 6 points per dollar (1800 ÷ 300 = 6). Once you know the unit rate, you can scale up or down to find any missing value. Proportions work because the relationship between points and dollars stays constant.

Quick Tip

Find the unit rate first: 1800 ÷ 300 = 6 points per dollar. Then divide the points earned by the rate: 600 ÷ 6 = $100. This shortcut is faster than cross multiplying!

Common Mistake

Students often flip the ratio and set up the proportion as points-to-dollars on one side but dollars-to-points on the other. Make sure both fractions are set up the same way (points on top, dollars on bottom) before cross multiplying.