High School

Verna shipped three packages to Chicago. If the packages weighed \( 12 \frac{1}{2} \), \( 35 \frac{1}{4} \), and \( 41 \frac{7}{20} \) pounds, what was the total weight?

A. \( 89 \frac{1}{10} \) pounds
B. \( 87 \frac{7}{10} \) pounds
C. \( 84 \frac{13}{20} \) pounds
D. \( 89 \frac{19}{20} \) pounds

Answer :

Final answer:

Option a. By converting mixed numbers to improper fractions with a common denominator and adding them together, we find that the total weight of the packages is 89 1/10 pounds.

Explanation:

To determine the total weight of Verna's packages shipped to Chicago, we must add the weights of all three packages: 12 1/2 pounds, 35 1/4 pounds, and 41 7/20 pounds. The first step is to convert all of these mixed numbers into improper fractions so they can be added together easily. Here is how we do it step by step:

Convert each mixed number to an improper fraction:

12 1/2 = 25/2

35 1/4 = 141/4

41 7/20 = 827/20

Find a common denominator (in this case, 20, since it is the least common multiple of 2, 4, and 20).

Convert fractions to have the common denominator:

25/2 = 250/20

141/4 = 705/20

Add the fractions:

250/20 + 705/20 + 827/20 = 1782/20

Convert the resulting improper fraction back to a mixed number:

1782/20 = 89 with a remainder of 2,

which gives us 89 2/20 or 89 1/10 when simplified.

Thus, the total weight of the packages is option a. 89 1/10 pounds.

Answer:

A

Step-by-step explanation:

1st package weighs [tex]12\dfrac{1}{2}[/tex] pounds;

2nd package weighs [tex]35\dfrac{1}{4}[/tex] pounds;

3rd package weighs [tex]41\dfrac{7}{20}[/tex] pounds;

First, add whole numbers:

[tex]12+35+41=88[/tex]

Now add fractions:

[tex]\dfrac{1}{2}+\dfrac{1}{4}+\dfrac{7}{20}=\dfrac{10}{20}+\dfrac{5}{20}+\dfrac{7}{20}=\dfrac{10+5+7}{20}=\dfrac{22}{20}=\dfrac{11}{10}=1\dfrac{1}{10}[/tex]

So, the total weight is

[tex]88+1\dfrac{1}{10}=89\dfrac{1}{10}\ pounds[/tex]