coffee shop sells small and large coffee. Each day they sell 510 cups of coffee. If the shop sells 3 times as many large cups as small cups of coffee, How many cups of each size do they sell daily?

L = 3S

L + S = 510

Substitute 3S for L in the second equation and solve for S. Insert that value into the first equation to solve for L. Check by putting both values into the second equation.

Let's represent the number of small cups as "S" and the number of large cups as "L".

According to the given information, the coffee shop sells a total of 510 cups of coffee daily. So we can write the equation:

S + L = 510

We are also told that the shop sells 3 times as many large cups as small cups, which means:

L = 3S

Now we can substitute the value of L from the second equation into the first equation:

S + 3S = 510

Combining the like terms:

4S = 510

Dividing both sides by 4:

S = 510/4
S = 127.5

However, we can't have a fraction of a cup, so let's round it to the nearest whole number:

S ≈ 128

Now, we can substitute the value of S back into the second equation to find L:

L = 3S
L = 3(128)
L = 384

Therefore, the coffee shop sells 128 small cups and 384 large cups daily.

To solve this problem, let's assign variables to the unknown quantities. Let's call the number of small coffee cups sold per day "x" and the number of large coffee cups sold per day "y".

From the information given, we know that each day they sell a total of 510 cups of coffee. Therefore, we can write an equation based on this information:

x + y = 510 (Equation 1)

We are also told that the shop sells 3 times as many large cups as small cups. Mathematically, this can be expressed as:

y = 3x (Equation 2)

Now we have a system of equations consisting of Equation 1 and Equation 2. We can solve this system to find the values of x and y.

Substituting Equation 2 into Equation 1, we get:

x + 3x = 510

Combining like terms, we have:

4x = 510

Dividing both sides by 4:

x = 510 / 4
x = 127.5

Since we're dealing with cups of coffee, the number of small cups sold cannot be in decimal form. Therefore, we can conclude that the shop sells 127 small cups per day.

To find the number of large cups sold, we substitute the value of x into Equation 2:

y = 3(127)
y = 381

Therefore, the coffee shop sells 127 small cups and 381 large cups daily.