This should be something I remember doing, but I can't.
What's given is $$ .15 = .7(.1)+.4a + .2b $$ and that $$.7 + a + b = 1$$
The answers on the solution sheet is $a = .1$, $ b = .2$
Can someone walk me through this and explain how to get a and b? thanks
edit: you guys were right. it should have been .4a and .2b
If $0.7+a+b=1$ then $a = 1 - b-0.7 = 0.3-b$. Therefore you can put $0.3-b$ in place of $a$.
\begin{align} 0.15 & = 0.07 +0.4a+ 0.2b \\[10pt] 0.15 & = 0.07 +0.4(\cdots)+0.2b \\[10pt] 0.15 & = 0.07 +0.4(0.3-b)+0.2b \end{align}
The last equation has only one unknown quantity. After you find that, then you can use $a=0.3-b$ to find $a$.