Let's build the equation counting how many x's and 1's are there on each side.
On the left hand side we have 5x's and 8 1's, for a total of 
On the left hand side we have 3x's and 10 1's, for a total of 
So, the equation we want to solve is
Subtract 3x from both sides:
Subtract 8 from both sides:
Divide both sides by 2:
Answer:
Day 6
Step-by-step explanation:
Every 3 days 1 pound of hay is used every day 1 pound of grain is used. There are 10 pounds of grain and 8 pounds of hay. On the 6th day there are 6 pounds of hay left and 6 pounds of grain left.
Answer:
7/10
Step-by-step explanation:
red + green = 50 + 20 = 70 marbles
Total marbles = 50 + 30 + 20 = 100 marbles
P(red or green) = 70/100
P(red or green) = 7/10
A good place to start is to set 
to y. That would mean we are looking for 
to be an integer. Clearly, 
, because if y were greater the part under the radical would be a negative, making the radical an imaginary number, not an integer. Also note that since 
is a radical, it only outputs values from ![[0,\infty]](https://tex.z-dn.net/?f=%20%5B0%2C%5Cinfty%5D%20)
, which means y is on the closed interval: ![[0,120]](https://tex.z-dn.net/?f=%20%5B0%2C120%5D%20)
.
With that, we don't really have to consider y anymore, since we know the interval that is on.
Now, we don't even have to find the x values. Note that only 11 perfect squares lie on the interval , which means there are at most 11 numbers that x can be which make the radical an integer. All of the perfect squares are easily constructed. We can say that if k is an arbitrary integer between 0 and 11 then:
Which is strictly positive so we know for sure that all 11 numbers on the closed interval will yield a valid x that makes the radical an integer.
(2 x 1,000) + (9 x 100) + (9 x 1)
Always check the place values by looking at the number (2,909) and you can figure out what number to multiply it by. Guess and check if you can’t recognize it right away.
