Equation is y = 59 - x. Use your equation to find the solution. He has 25 dimes. He has 34 half dollars.
Here is an equation that can be used to solve the problem:
0.1x + 0.5y = 19.5
where:
x is the number of dimes
y is the number of half-dollars
This equation represents the fact that the total value of the coins is $19.50. We can solve for x and y using this equation.
Here are the steps to solve for x and y:
1. Solve the first equation for y:
y = 59 - x
2. Substitute this equation into the second equation:
0.1x + 0.5(59 - x) = 19.5
3. Simplify the equation:
0.1x + 29.5 - 0.5x = 19.5
4. Combine like terms:
-0.4x + 29.5 = 19.5
5. Subtract 29.5 from both sides:
-0.4x = -10
6. Divide both sides by -0.4:
x = 25
Therefore, Paul has 25 dimes.
Now that we know x, we can plug it back into the first equation to find y:
25 + y = 59
7. Subtract 25 from both sides:
y = 34
Therefore, Paul has 34 half dollars.
Question:
Paul has a change jar that contains only dimes and half dollars. He has 59 coins which add up to a total of $19.50. How many of each type of coin does he have? A). Enter an equation using the information as it is given that can be solved to find the solution to this problem. Use x as your variable to represent the number of dimes. Note: The equation should not include any numbers that do not appear in the original problem. Equation: ____________________ Use your equation to find the solution. He has __________dimes. He has _________ half dollars.