This is the only question in this section. Question Watch Video Show Sxamples Lincoln has \$0.90 worth of nickels and dimes. He has a total of 14 nickels and dimes altogether. By following the steps below, determine the number of nickels, $$ x $$, and the number of dimes, $$ y $$, that Lincoln has. Determine three ways to have a total of 14 coins: deally $$ \square $$

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To solve this problem, we can set up a system of equations based on the information given. Let's denote the number of nickels as $$ x $$ and the number of dimes as $$ y $$.

Given:
1. The total value of nickels and dimes is $0.90.
2. The total number of nickels and dimes is 14.

We can set up the following system of equations:
1. $$ 0.05x + 0.10y = 0.90 $$ (Equation 1: Total value of nickels and dimes)
2. $$ x + y = 14 $$ (Equation 2: Total number of nickels and dimes)

Now, we can solve this system of equations to find the values of $$ x $$ and $$ y $$.

Let's solve the system of equations.
Solve the system of equations by following steps:
- step0: Solve using the substitution method:
  $$\left\{ \begin{array}{l}0.05x+0.1y=0.9\x+y=14\end{array}ight.$$
- step1: Solve the equation:
  $$\left\{ \begin{array}{l}0.05x+0.1y=0.9\x=14-y\end{array}ight.$$
- step2: Substitute the value of $$x:$$
  $$0.05\left(14-yight)+0.1y=0.9$$
- step3: Simplify:
  $$0.7+0.05y=0.9$$
- step4: Move the constant to the right side:
  $$0.05y=0.9-0.7$$
- step5: Subtract the numbers:
  $$0.05y=0.2$$
- step6: Divide both sides:
  $$\frac{0.05y}{0.05}=\frac{0.2}{0.05}$$
- step7: Divide the numbers:
  $$y=4$$
- step8: Substitute the value of $$y:$$
  $$x=14-4$$
- step9: Calculate:
  $$x=10$$
- step10: Calculate:
  $$\left\{ \begin{array}{l}x=10\y=4\end{array}ight.$$
- step11: Check the solution:
  $$\left\{ \begin{array}{l}x=10\y=4\end{array}ight.$$
- step12: Rewrite:
  $$\left(x,yight) = \left(10,4ight)$$
The solution to the system of equations is $$ x = 10 $$ and $$ y = 4 $$.

Therefore, Lincoln has 10 nickels and 4 dimes.

Now, let's determine three ways to have a total of 14 coins:
1. 10 nickels and 4 dimes
2. 14 dimes
3. 14 nickels
Lincoln has 10 nickels and 4 dimes. Three ways to have a total of 14 coins are: 1. 10 nickels and 4 dimes 2. 14 dimes 3. 14 nickels

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