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?
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.
