Betty invested $10,000 at the beginning of the year. At the end of the year, her investment was worth $12,000. Ronnie also invested in the same fund. At the beginning of the year, he invested $15,000. How much will his investment be worth at the end of the year?
  1. $18,000
  2. $20,000
  3. $21,000
  4. $19,500
  5. $16,200
Explanation
Answer: $18,000. One way to do this is to see quickly that the the investment went up 20%. @0% of $15,000 is $3,000.

$3,000 + $15,000 is $18,000.

This problem can also be solved as a ratio with a direct relationship, and actually can be done mentally.

Think: 10/12 = 15/x.

Visualize cross-multiplying so that 10x = 12x15.

In an earlier problem, we learned that to multiply two-digit numbers mentally, we should halve and double. In this case 12x15 = 6x30=180.

So 10x =180, and x=18. Therefore, Ronnie’s investment is worth $18,000 at the end of the year.

Key Takeaway: Knowing how to set up and manipulate ratios and proportions and having mental computation strategies will allow you to calculate multi-step problems in your head.
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