Andre and Jillian were shopping at the same grocery store for bottles of sports drinks for their kickball teams. Andre bought 3

Question

packs of bottled drinks, plus 11
single bottles. Jillian purchased 5
packs, plus 3
singles. Andre and Jillian discovered that they had purchased the same number of bottles. How many bottles were in each of the packs? (All of the packs have the same number of bottles.)

Answer 1

Let \( x \) be the number of bottles in each pack.

Andre's total number of bottles can be expressed as: \[ 3x + 11 \] Jillian's total number of bottles can be expressed as: \[ 5x + 3 \]

Since Andre and Jillian purchased the same number of bottles, we can set their total bottle counts equal to each other: \[ 3x + 11 = 5x + 3 \]

Next, we can solve for \( x \). Start by rearranging the equation to isolate \( x \): \[ 3x + 11 - 3 = 5x \] \[ 8 = 5x - 3x \] \[ 8 = 2x \] \[ x = \frac{8}{2} = 4 \]

Now we have determined that each pack contains \( \boxed{4} \) bottles.

To verify, we can calculate the total number of bottles Andre and Jillian bought:

For Andre: \[ 3 \text{ packs} \times 4 \text{ bottles/pack} + 11 \text{ singles} = 12 + 11 = 23 \text{ bottles} \]

For Jillian: \[ 5 \text{ packs} \times 4 \text{ bottles/pack} + 3 \text{ singles} = 20 + 3 = 23 \text{ bottles} \]

Both totals are indeed 23, confirming that our solution is correct. Each pack contains \( \boxed{4} \) bottles.