Yesterday, Castle Mountain Fashions had seven less than three-fourths of its sales transactions paid for by credit cards. If 209 transactions were charged, how many total transactions took place?

Question

Yesterday, Castle Mountain Fashions had seven less than three-fourths of its sales transactions paid for by credit cards. If 209 transactions were charged, how many total transactions took place?

Answer 1

X = total transactions.

3x/4 - 7 = 209..
X = ?

Answer 2

Let's break down the information given step by step:

Step 1: Let's call the unknown total number of transactions as "x".

Step 2: Three-fourths of the total transactions were paid for by credit cards. So, we can write this as an equation: (3/4) * x.

Step 3: Now, it is mentioned that Castle Mountain Fashions had seven less than three-fourths of its transactions paid for by credit cards. So, we subtract 7 from the credit card transactions: (3/4) * x - 7.

Step 4: The result of step 3 is given as 209 transactions, which we can write as an equation: (3/4) * x - 7 = 209.

Step 5: Now, we can solve this equation to find the value of "x".

Let's solve step 4:
(3/4) * x - 7 = 209

Step 6: Add 7 to both sides of the equation to isolate the term with "x":
(3/4) * x = 216

Step 7: Multiply both sides of the equation by 4/3 to get rid of the fraction:
x = 4/3 * 216

Step 8: Calculate the value:
x = 288

Therefore, the total number of transactions that took place is 288.

Answer 3

To find the total number of transactions, you need to determine the total number of transactions paid for by credit cards.

Let's break down the given information step by step:

1. "Castle Mountain Fashions had seven less than three-fourths of its sales transactions paid for by credit cards." This means that three-fourths of the total transactions were paid for by credit cards, minus seven.

Let's represent the total number of transactions as "x." In this case, three-fourths of x is (3/4)x, and seven less than that is (3/4)x - 7.

2. We are also given that 209 transactions were charged. This represents the value of (3/4)x - 7, which equals 209.

Now, we can set up the equation and solve for x:

(3/4)x - 7 = 209

First, let's get rid of the fraction by multiplying every term by 4 to clear the denominator:

4 * [(3/4)x - 7] = 4 * 209
3x - 28 = 836

Next, we isolate x by adding 28 to both sides of the equation:

3x = 836 + 28
3x = 864

Finally, divide both sides of the equation by 3 to solve for x:

x = 864 / 3
x = 288

Therefore, the total number of transactions that took place at Castle Mountain Fashions is 288.