last week at a festival, a man sold 3 times as many tie-dyed shirts as silk-screened shirts. He sold 148 shirts altoether. How many tie-dyed shirts did he sell?
Let's solve this step-by-step:
Step 1: Assign variables
Let's call the number of tie-dyed shirts "x" and the number of silk-screened shirts "y".
Step 2: Express the problem in equations
From the problem, we know that the man sold 3 times as many tie-dyed shirts as silk-screened shirts, so we can write the equation: x = 3y
We also know that the total number of shirts sold was 148, so we can write another equation: x + y = 148
Step 3: Solve the system of equations
Now we have a system of two equations with two variables:
x = 3y
x + y = 148
From the first equation, we can substitute x with 3y in the second equation:
3y + y = 148
4y = 148
y = 37
Step 4: Calculate the number of tie-dyed shirts
Now that we know the value of y, we can substitute it in the first equation to find x:
x = 3y
x = 3 * 37
x = 111
Therefore, the man sold 111 tie-dyed shirts.
To find the number of tie-dyed shirts the man sold, we can set up a system of equations. Let's say he sold x silk-screened shirts. According to the problem, he sold 3 times as many tie-dyed shirts as silk-screened shirts. Therefore, he sold 3x tie-dyed shirts.
The total number of shirts he sold is given as 148. So, we can set up the equation:
x + 3x = 148
Combining like terms, the equation becomes:
4x = 148
To isolate x, the variable representing the number of silk-screened shirts, we divide both sides of the equation by 4:
4x/4 = 148/4
x = 37
So, the man sold 37 silk-screened shirts. To find the number of tie-dyed shirts, we can substitute this value back into the equation:
3x = 3*37
3x = 111
Therefore, the man sold 111 tie-dyed shirts.
3x + x = 148
4x = 148
x = 37
He sold 37 silk-screen shirts.
Take it from there.