Investing: Inverse ETFs $($Exchange Traded Funds$)$ Inverse ETFs, sometimes referred to as "bear market" or "short" funds, are designed to deliver the opposite of the performance of the index or category they track, and so can be used by traders to bet against the stock market. The following table shows the performance of three such funds as of August $5,2015.$

Year$-$to$-$Date

Loss $(\%)$

MYY $($ProShares Short Midcap $400)6$

SH $($ProShares Short S&P $500)5$

REW $($ProShares UltraShort Technology$)7$

You invested a total of $$15,000$ in the three funds at the beginning of $2011,$ including an equal amount in SH and REW. Your year$-$to$-$date loss from the first two funds amounted to $$620.$ How much did you invest in each of the three funds?