there were ships with 3 masts and ships with 4 masts at the Tall ships exhibition. mille counted a total of 29 masts on the 8 ships he saw. how many of these ships have 4 masts
Let x be the number of ships with 3 masts.
Then, the number of ships with 4 masts is 8 - x.
Each ship with 3 masts has 3 masts.
Each ship with 4 masts has 4 masts.
The total number of masts is 3x + 4(8 - x) = 29.
Simplifying the equation, we get:
3x + 32 - 4x = 29
-x + 32 = 29
-x = -3
x = 3
So, there are 8 - x = 8 - 3 = <<8-3=5>>5 ships with 4 masts. Answer: \boxed{5}.
Let's solve the problem step by step:
Step 1: Assign variables.
Let's say the number of ships with 3 masts is "x" and the number of ships with 4 masts is "y".
Step 2: Write equations based on the given information.
From the information given, we can write two equations:
Equation 1: x + y = 8 (since there were a total of 8 ships)
Equation 2: 3x + 4y = 29 (since there were a total of 29 masts)
Step 3: Solve the equations.
We can solve these equations using the method of substitution or elimination. Let's use the elimination method in this case:
Multiply Equation 1 by 3 to make the coefficients of "x" in both equations equal:
3(x + y) = 3(8) => 3x + 3y = 24
Subtract Equation 2 from the modified Equation 1:
(3x + 3y) - (3x + 4y) = 24 - 29
3x + 3y - 3x - 4y = -5y = -5
Step 4: Solve for y.
Simplifying the equation, we get:
-5y = -5
Divide both sides of the equation by -5:
y = 1
Step 5: Substitute the value of y back into Equation 1 to find x.
x + 1 = 8
Subtract 1 from both sides of the equation:
x = 7
Step 6: Interpret the solution.
The solution is x = 7 and y = 1. Therefore, there were 7 ships with 3 masts and 1 ship with 4 masts at the tall ships exhibition.