Fido gets 2 doggy treats every time he sits and 4 doggy treats every time he rolls over. Throughout the week, he has sat 6 times as often as he has rolled over. In total, he has earned 80 doggy treats. How many times has Fido rolled over??
2 s + 4 r = 80
but s = 6 r
so
16 r = 80
r = 5
To solve this problem, we need to set up a system of equations. Let's start by defining the variables:
Let's say the number of times Fido sits is represented by 's', and the number of times Fido rolls over is represented by 'r'.
According to the given information:
1. Fido gets 2 treats every time he sits, so he earns a total of 2s treats from sitting.
2. Fido gets 4 treats every time he rolls over, so he earns a total of 4r treats from rolling over.
3. Throughout the week, he has sat 6 times as often as he has rolled over, so we have the equation s = 6r.
4. In total, Fido has earned 80 doggy treats, so we have the equation 2s + 4r = 80.
Now we can solve this system of equations.
Substituting the value of 's' from the equation s = 6r into the equation 2s + 4r = 80, we get:
2(6r) + 4r = 80
12r + 4r = 80
16r = 80
Dividing both sides of the equation by 16, we get:
r = 5
Therefore, Fido has rolled over 5 times.