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Giovanna,frances, and their dad each carried a 10-pound bag of soil into the backyard. After putting soil in the first flower bed, Giovanna's bag was 5/8 full, Frances's bag was 2/5 full, and their dads was 3/4 full. How many pounds of soil did they put in the first flower bed altogether?

Respuesta :

xbeatdroperzx

Answer:

I got 1.7 Lbs.

Step-by-step explanation:

i turned the fractions into decimals and added them up

BladeRunner212

12.25 pounds of soil  (or 12¹/₄ pounds).

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 [tex]\frac{5}{8}[/tex] full,  
  • Frances bag was [tex]\frac{2}{5}[/tex] full, and
  • Their dad's was [tex]\frac{3}{4}[/tex] 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.

  • [tex]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[/tex]. [tex]\boxed{1 \ unit = \frac{10}{8} = 1.25 \ pounds}[/tex]
  • [tex]France's: \boxed{\frac{10}{5}}\boxed{\frac{10}{5}}\boxed{\frac{10}{5}}\boxed{\frac{10}{5}}\boxed{\frac{10}{5}} = 10 \ pounds[/tex]. [tex]\boxed{1 \ unit = \frac{10}{5} = 2 \ pounds}[/tex]
  • [tex]Dad's: \boxed{\frac{10}{4}}\boxed{\frac{10}{4}}\boxed{\frac{10}{4}}\boxed{\frac{10}{4}} = 10 \ pounds[/tex]. [tex]\boxed{1 \ unit = \frac{10}{4} = 2.5 \ pounds}[/tex]

Now consider the final step.

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

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

We add up to be [tex]\boxed{ \ 3.75 + 6 + 2.5 = 12.25 \ }[/tex].

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

- - - - - - - - - -

Quick Steps:

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

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

[tex]\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 \ }[/tex]

[tex]\boxed{ \ \bigg(\frac{15}{40} + \frac{24}{40} + \frac{10}{40} \bigg) \times 10 \ pounds \ }[/tex]

[tex]\boxed{ \ \frac{49}{40} \times 10 \ pounds \ }[/tex]

[tex]\boxed{ \ \frac{49}{4} \ pounds \ }[/tex]

[tex]\boxed{ \ \frac{48}{4} + \frac{1}{4} \ pounds \ }[/tex]

[tex]\boxed{ \ 12\frac{1}{4} \ pounds \ }[/tex]

[tex]\boxed{\boxed{ \ 12.25 \ pounds \ }}[/tex]

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