An alloy consists of nickel, zinc, and copper in the ratio 2:7:9. How many pounds of nickel have to be used to create alloy that contains 4.9 lb of zinc?
Let the weight of the alloy be $2x+7x+9x=18x,$ which we set to be a value equal to the weight of the alloy. This means that \begin{align*}
\frac{7}{18}&=\frac{4.9}{18x} \\
14x&=4.9 \\
x&=\boxed{\frac{7}{140} \text{ pounds}}.
\end{align*}
No. Please try again.
Apologies for the mistake. Let the total weight of the alloy be $x$ pounds.
Since the ratio of nickel to zinc to copper is 2:7:9, we have 2 parts of nickel, 7 parts of zinc, and 9 parts of copper.
The weight of zinc in the alloy is $\frac{7}{2}$ times the weight of nickel. So if the weight of zinc is 4.9 pounds, the weight of nickel is $\frac{2}{7} \times 4.9 = \boxed{1.4}$ pounds.
Jane and Jill collect stamps. The ratio of Jane's coins to Jill's coins is 5:4. If Jane loses 15 of her coins, Jane and Jill will have the same number of coins in their collection. How many coins do the girls currently have together?
Let the number of coins Jane has be 5x and the number of coins Jill has be 4x.
If Jane loses 15 coins, she will have 5x - 15 coins.
Since Jane and Jill will then have the same number of coins, we have the equation 5x - 15 = 4x.
Solving this equation, we find x = 15.
Therefore, the number of coins Jane has is 5x = 5 * 15 = 75, and the number of coins Jill has is 4x = 4 * 15 = 60.
The total number of coins the girls currently have together is 75 + 60 = <<75+60=135>>135. Answer: \boxed{135}.