Wesley is making a patio from stones of two sizes, 5 inches wide and 10 inches wide. He wants to begin and end his pattern with a 10-inch stone so there will be one more of the 10-inch stones than of the 5-inch stones . His patio will be 130 inches wide
To solve this problem, we need to determine the number of each stone size that Wesley needs. Let's start by assigning variables to represent the number of 10-inch stones and 5-inch stones.
Let's let x represent the number of 10-inch stones and y represent the number of 5-inch stones.
Based on the information given, we know that Wesley wants to begin and end his pattern with a 10-inch stone. This means that the length of a 10-inch stone, when added together, should be divisible by 10.
The length of a 10-inch stone is 10 inches, so the total length of all the 10-inch stones can be represented as 10x.
Similarly, the length of a 5-inch stone is 5 inches, so the total length of all the 5-inch stones can be represented as 5y.
Wesley wants there to be one more 10-inch stone than 5-inch stones, so we can write an equation to represent this:
x = y + 1
We also know that the total width of the patio is 130 inches. Since the width is obtained by adding all the stone widths together, we can set up another equation:
10x + 5y = 130
Now we have a system of two equations:
x = y + 1 (equation 1)
10x + 5y = 130 (equation 2)
We can solve this system of equations using substitution or elimination.
Using substitution:
From equation 1, we can substitute y + 1 for x in equation 2:
10(y + 1) + 5y = 130
10y + 10 + 5y = 130
15y + 10 = 130
15y = 120
y = 8
Using equation 1, we can then find x:
x = y + 1
x = 8 + 1
x = 9
Therefore, Wesley needs 9 stones that are 10 inches wide and 8 stones that are 5 inches wide in order to create a patio that is 130 inches wide.
I assume you want to know how many stones it will take to pave 130 inches.
10(x+1) + 5x = 130
15x + 10 = 130
x = 8
so, 8 5" and 9 10" = 40+90 = 130"