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.
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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
