A mixed apple vendor starts out with $28 \frac{2}{5}$ apples, sells $5 \frac{1}{2}$ apples to Bob, and then sells $7 \frac{1}{3}$ apples to Jane. After these two sales, how many apples does the vendor have left (expressed as a mixed number)?

[tex]28\frac{2}{5} - 5\frac{1}{2} -7\frac{1}{3} \\\frac{28 \cdot 5+2}{5} - \frac{5 \cdot 2+1}{2} -\frac{7 \cdot 3+1}{3} \\\\\frac{142}{5} - \frac{11}{2} -\frac{22}{3} \\[/tex]

Make denominators same. LCD 30

[tex]\frac{142}{5} - \frac{11}{2} -\frac{22}{3} \\\\\frac{852}{30} - \frac{165}{30} -\frac{220}{30} \\\\\\\frac{467}{30} \\\\15\frac{17}{30}[/tex]

ariawoolley ariawoolley · Answer 2 · 2020-08-23T18:30:20+02:00

Answer:

15 17/30

Step-by-step explanation:

We want to find 28 2/5 - 5 1/2 - 7 1/3. We convert each of these three mixed numbers to fractions. First, we have 28 2/5 = 28 + 2/5 = {28*5}/{5} + 2/5 = {140+2}/{5} = 142/5.

Next, 5 1/2 = 5 + 1/2 = {5*2}/{2} + 1/2 = {10+1}/{2} = 11/2.

Lastly, 7 1/3 = 7 + 1/3 = {3*7}/{3} + 1/3 = {21+1}/{3} = 22/3.

Plugging these fractions into the original expression, we simplify: 142/5 - 11/2 - 22/3 by using the least common denominator of 30. So, 142/5 = 142 852/30$. Next, 11/2 = 165/30. Then, 22/3 = 220/30}. Combining these into the expression we are solving for, we get: 852/30 - 165/30 - 220/30 = {852 - 165 - 220}/30 = 467/30.

Finally, we convert this fraction to a mixed number. 467/30 = {15 * 30 + 17}/{30} = {15*30}/{30} + 17/30 = 15 + 17/30. This gives us our final answer: 15 17/30$.