Six more than the product of seven and a number is 55.

Question

Which equation and solution correctly represent this sentence?

7 x + 6 = 55; x = 7
x/7+ 6 = 55; x = 49
x/7 + 6 = 55; x = 7
7 x + 6 = 55; x = 49

Answer 1

Let's break down the sentence "Six more than the product of seven and a number is 55":

1. "The product of seven and a number" can be represented as \( 7x \) (where \( x \) is the number).
2. "Six more than this product" translates to \( 7x + 6 \).
3. "is 55" means we set the expression equal to 55.

Putting all of this together, we form the equation:

\[ 7x + 6 = 55 \]

Now, let's solve this equation step by step:

1. Subtract 6 from both sides: \[ 7x = 55 - 6 \] \[ 7x = 49 \]

2. Divide both sides by 7: \[ x = \frac{49}{7} \] \[ x = 7 \]

Now let's review the given options:

1. \( 7x + 6 = 55; x = 7 \) (This one is correct.)
2. \( \frac{x}{7} + 6 = 55; x = 49 \) (This one is incorrect.)
3. \( \frac{x}{7} + 6 = 55; x = 7 \) (This one is incorrect.)
4. \( 7x + 6 = 55; x = 49 \) (This one is incorrect.)

The correct equation and solution is:

\( 7x + 6 = 55; x = 7 \).