QuestionAngie sells handmade bracelets at craft fairs. She bought 2 packs of charms. One pack has 150 small charm and 60 large charms. The other pack has the same ratio of small to large charms. The second pack has 50 small charms.
How many large charms are in the second pack? $\square$ large charms

Studdy Solution

STEP 1

1. Angie sells handmade bracelets at craft fairs.
2. She bought 2 packs of charms.
3. The first pack contains 150 small charms and 60 large charms.
4. The second pack has the same ratio of small to large charms as the first pack.
5. The second pack contains 50 small charms.
6. We need to find the number of large charms in the second pack.

STEP 2

1. Determine the ratio of small to large charms in the first pack.
2. Use the ratio to find the number of large charms in the second pack.

STEP 3

Determine the ratio of small to large charms in the first pack.
The first pack has 150 small charms and 60 large charms. The ratio of small to large charms is:
$\text{Ratio} = \frac{150 \text{ small charms}}{60 \text{ large charms}} = \frac{150}{60} = \frac{5}{2}$

STEP 4

Use the ratio to find the number of large charms in the second pack.
Let $x$ be the number of large charms in the second pack. The second pack has 50 small charms, and the ratio of small to large charms should be the same as the first pack, which is $\frac{5}{2}$ .
Set up the equation:
$\frac{50 \text{ small charms}}{x \text{ large charms}} = \frac{5}{2}$
Cross-multiply to solve for $x$ :
$5x = 50 \times 2$
$5x = 100$
Divide both sides by 5:
$x = \frac{100}{5} = 20$
There are $\boxed{20}$ large charms in the second pack.

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