Question

Suppose restaurant​ A's chicken salad contains 88 more grams of fat than restaurant​ B's chicken salad. Find the number of grams of fat in each salad if there are 6464 grams of fat in the two salads by solving the equation x plus left parenthesis x plus 8 right parenthesis equals 64x+(x+8)=64​, where x represents the number of fat grams in the restaurant​ B's chicken salad and x plus 8x+8 represents the number of fat grams in restaurant​ A's chicken salad.

Answer 1

We need to find the number of grams of fat in restaurant A's and restaurant B's chicken salads based on the information provided. You have described an equation that relates the grams of fat in each salad.

Let:
- \( x \): the number of grams of fat in restaurant B's chicken salad.
- \( x + 88 \): the number of grams of fat in restaurant A's chicken salad.

According to the problem, the sum of the fats in both salads is 6464 grams, so we can set up the equation as follows:

\[
x + (x + 88) = 6464
\]

Now, combine like terms:

\[
2x + 88 = 6464
\]

Next, we will subtract 88 from both sides:

\[
2x = 6464 - 88
\]

\[
2x = 6376
\]

Now, we will divide both sides by 2 to solve for \( x \):

\[
x = \frac{6376}{2}
\]

\[
x = 3188
\]

Now that we have \( x \), which represents the grams of fat in restaurant B's chicken salad, we can find the grams of fat in restaurant A's chicken salad:

\[
x + 88 = 3188 + 88 = 3276
\]

Thus, we conclude:

- The number of grams of fat in restaurant B's chicken salad is **3188 grams**.
- The number of grams of fat in restaurant A's chicken salad is **3276 grams**.