Question

Giovanna,Frances, and their dad each carried a ten pound bag of soil into the back yard. After putting soil in the first flower bed, Giovanna's bag was 5/8 full, Frances bag was 2/5 full, and their dad's was 3/4 full. How many pounds of soil did they put in the first flower bed all together (how to work it out)

Answer 1

First find the common denominator
5/8=25/40
2/5=16/40
3/4=30/40
Next you can cross multiply
25/40=x/10 pounds
16/40=x/10 pounds
30/40=x/10 pounds
First
25(10)/40= 6.25 pounds
16(10)/40= 4pounds
30(10)/40= 7.5 pounds
These are the amounts that were left in the bag

10-6.25=3.75
10-4=6
10-7.5=2.5

3.75+6+2.5= 12.25

All together they put 12.25 pounds of soil in the flower bed

Answer 2

12.25 pounds of soil

Further explanation

Given:

Giovanna, Frances, and their dad each carried a 10-pound bag of soil into the back yard. After putting soil in the first flower bed:

• Giovanna's bag was $\frac{5}{8}$ full,
• Frances bag was $\frac{2}{5}$ full, and
• their dad's was $\frac{3}{4}$ full.

Question:

How many pounds of soil did they put in the first flower bed altogether?

The Process:

Let us create each diagram for each of their 10-pound bags of soil.

• $Giovanna's: \boxed{\frac{10}{8}}\boxed{\frac{10}{8}}\boxed{\frac{10}{8}}\boxed{\frac{10}{8}}\boxed{\frac{10}{8}}\boxed{\frac{10}{8}}\boxed{\frac{10}{8}}\boxed{\frac{10}{8}} = 10 \ pounds$. $\boxed{1 \ unit = \frac{10}{8} = 1.25 \ pounds}$
• $France's: \boxed{\frac{10}{5}}\boxed{\frac{10}{5}}\boxed{\frac{10}{5}}\boxed{\frac{10}{5}}\boxed{\frac{10}{5}} = 10 \ pounds$. $\boxed{1 \ unit = \frac{10}{5} = 2 \ pounds}$
• $Dad's: \boxed{\frac{10}{4}}\boxed{\frac{10}{4}}\boxed{\frac{10}{4}}\boxed{\frac{10}{4}} = 10 \ pounds$. $\boxed{1 \ unit = \frac{10}{4} = 2.5 \ pounds}$

Let us calculate how many pounds of soil did they put in the first flower bed altogether. After putting soil,

• Giovanna's bag was $\frac{5}{8}$ full or 5 of 8 units. Hence, Giovanna put 3 of 8 units, or $\boxed{\boxed{ \ 3 \times 1.25 \ pounds = 3.75 \ pounds \ }}$.
• Frances's bag was $\frac{2}{5}$ full or 2 of 5 units. Hence, Frances put 3 of 5 units, or $\boxed{\boxed{ \ 3 \times 2 \ pounds = 6 \ pounds \ }}$.
• Dad's bag was $\frac{3}{4}$ full or 3 of 4 units. Hence, Dad put 1 of 4 units, or $\boxed{\boxed{ \ 1 \times 2.5 \ pounds = 2.5 \ pounds \ }}$.

We add up to be $\boxed{ \ 3.75 + 6 + 2.5 = 12.25 \ }$.

Thus, they put 12.25 pounds of soil in the first flower bed altogether.

- - - - - - - - - -

Quick Steps:

$\boxed{ \ \Bigg(\bigg(1 - \frac{5}{8}\bigg) + \bigg(1 - \frac{2}{5}\bigg) + \bigg(1 - \frac{3}{4} \bigg) \Bigg) \times 10 \ pounds \ }$

Least common multiple (LCM) of 8, 5, and 4 are 40.

$\boxed{ \ \Bigg(\bigg(\frac{40}{40} - \frac{25}{40}\bigg) + \bigg(\frac{40}{40} - \frac{16}{40}\bigg) + \bigg(\frac{40}{40} - \frac{30}{40} \bigg) \Bigg) \times 10 \ pounds \ }$

$\boxed{ \ \bigg(\frac{15}{40} + \frac{24}{40} + \frac{10}{40} \bigg) \times 10 \ pounds \ }$

$\boxed{ \ \frac{49}{40} \times 10 \ pounds \ }$

$\boxed{ \ \frac{49}{4} \ pounds \ }$

$\boxed{ \ \frac{48}{4} + \frac{1}{4} \ pounds \ }$

$\boxed{ \ 12\frac{1}{4} \ pounds \ }$

$\boxed{\boxed{ \ 12.25 \ pounds \ }}$

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Keywords: Giovanna, Frances, their dad, each carried, a 10-pound bag of soil, into the back yard, after putting soil, in the first flower bed, 5/8 full, 2/5, 3/4, how many, they put, altogether