in a hardware store the ratio of shovels to rake is 3:5.If there are 10 more rakes than shovels how many rakes are there in the hardware store?
3:5::(r-10)/r
5(r-10)=3r solve for r.
To determine the number of rakes in the hardware store, we can start by assigning variables to represent the number of shovels and rakes. Let's call the number of shovels "x" and the number of rakes "y".
According to the given ratio, the ratio of shovels to rakes is 3:5. This can be written as:
x:y = 3:5
We are also told that there are 10 more rakes than shovels, which means:
y = x + 10
To find the value of "y" (the number of rakes), we can substitute the relationship between "y" and "x" into the ratio equation:
x:y = 3:5
x:(x+10) = 3:5
Now, let's cross-multiply:
5x = 3(x+10)
5x = 3x + 30
Subtracting 3x from both sides:
2x = 30
Dividing both sides by 2:
x = 15
So, there are 15 shovels in the hardware store.
Now, we can substitute this value back into the equation for "y" to find the number of rakes:
y = x + 10
y = 15 + 10
y = 25
Therefore, there are 25 rakes in the hardware store.