If Ann and Betty shared a sum of money in the ratio 2:3 and Ann received $120, what was Betty's share?

• A. $180
• B. $150
• C. $200
• D. $160

Answer: (A)

To determine Betty's share in the money that Ann and Betty shared, we first analyze the ratio in which the money was divided. The ratio of Ann's share to Betty's share is 2:3. This means that for every 2 parts that Ann receives, Betty receives 3 parts.

Given that Ann received $120, we can calculate the amount that corresponds to one part of the ratio. Since Ann receives 2 parts, we can find the value of one part by dividing her share by 2:

[

\text{Value of one part} = \frac{\text{Ann's share}}{2} = \frac{120}{2} = 60

]

Now, to find Betty's share, which corresponds to 3 parts of the total, we multiply the value of one part by 3:

[

\text{Betty's share} = 3 \times \text{Value of one part} = 3 \times 60 = 180

]

Thus, Betty's share of the money is $180. This calculation clearly illustrates how the parts of the ratio translate into actual dollar amounts based on Ann's known share.