Ryan is building matchstick square sequences, as shown ( first figure used 4, second figure used 7, third figure used 10, and the forth figure used 13). He used 599 matchsticks to form the last two figures in his sequences. How many matchsticks did he use in each of the last two figures?

Question

Ryan is building matchstick square sequences, as shown ( first figure used 4, second figure used 7, third figure used 10, and the forth figure used 13). He used 599 matchsticks to form the last two figures in his sequences. How many matchsticks did he use in each of the last two figures?

Answer 1

To find out how many matchsticks Ryan used in each of the last two figures, let's first analyze the pattern in the matchstick square sequences.

From the given information, we can observe the following pattern:
- The first figure used 4 matchsticks (this is the starting point).
- The second figure used 7 matchsticks, which is an increment of 3 matchsticks from the first figure.
- The third figure used 10 matchsticks, which is again an increment of 3 matchsticks from the second figure.
- The fourth figure used 13 matchsticks, which is also an increment of 3 matchsticks from the third figure.

So, we can see that the number of matchsticks used in each figure is increasing by 3 as we move from one figure to the next.

Now, let's find the total number of matchsticks used in the last two figures.

The last two figures in the sequence are the third and fourth figures, which used 10 and 13 matchsticks, respectively. To find the total number of matchsticks used in these figures, we can simply add the number of matchsticks together: 10 + 13 = 23 matchsticks.

Now, we need to determine how many matchsticks were used in each of the figures individually.

Let's assume that the third figure used X matchsticks, and the fourth figure used Y matchsticks.

From the information given, we know that the sum of X and Y should be equal to 23 (the total number of matchsticks used in the last two figures).

Therefore, we have the equation: X + Y = 23.

However, we also have another piece of information that states the total number of matchsticks used in the last two figures is 599.

So, we have another equation: X + Y = 599.

Since we have two equations with the same variables (X and Y), we can solve this system of equations to find the values of X and Y.

Subtracting the first equation (X + Y = 23) from the second equation (X + Y = 599), we get: 0 = 576.

This equation has no valid solution. Therefore, it seems there is an error or inconsistency in the given information. Please double-check the information provided or provide additional details if available.