mark wants to paint a mural. He has 1 1/3 gallons of yellow paint, 1 1/4 gallons of green paint, and 7/8 gallon of blue paint. m
ark plans to use 3/4 of each paint color. how many gallons of paint will he have left after painting the mural
2 answers:
Mark has: 1 1/3 = 4/3 gallons of Yellow
1 1/4 = 5/4 gallons of Green
7/8 gallons of Blue.
Total = (4/3 + 5/4 + 7/8) LCM = 24
= (32 + 30 + 21)/24 = 83/24 Gallons of Paint in total.
If he used 3/4 of each, he would have (1 - 3/4) = 1/4 of each left.
Therefore gallons left = 1/4 * (83/24) = 83/96 gallons left.
= 0. 8646 gallons left in total.
we have
Yellow paint
![1\frac{1}{3} =(3*1+1)/3\\ \\ =\frac{4}{3} gal](https://tex.z-dn.net/?f=%201%5Cfrac%7B1%7D%7B3%7D%20%3D%283%2A1%2B1%29%2F3%5C%5C%20%5C%5C%20%3D%5Cfrac%7B4%7D%7B3%7D%20gal%20)
Find the
amount of yellow paint left after painting the mural
![(\frac{4}{3} -\frac{3}{4} )=(4*4-3*3)/12\\ \\ =\frac{7}{12} gal](https://tex.z-dn.net/?f=%20%28%5Cfrac%7B4%7D%7B3%7D%20-%5Cfrac%7B3%7D%7B4%7D%20%29%3D%284%2A4-3%2A3%29%2F12%5C%5C%20%5C%5C%20%3D%5Cfrac%7B7%7D%7B12%7D%20gal%20)
Green paint
![1\frac{1}{4} =(4*1+1)/4\\ \\ =\frac{5}{4} gal](https://tex.z-dn.net/?f=%201%5Cfrac%7B1%7D%7B4%7D%20%3D%284%2A1%2B1%29%2F4%5C%5C%20%5C%5C%20%3D%5Cfrac%7B5%7D%7B4%7D%20gal%20)
Find the
amount of green paint left after painting the mural
![(\frac{5}{4} -\frac{3}{4} )=(5-3)/4\\ \\ =\frac{2}{4} gal](https://tex.z-dn.net/?f=%20%28%5Cfrac%7B5%7D%7B4%7D%20-%5Cfrac%7B3%7D%7B4%7D%20%29%3D%285-3%29%2F4%5C%5C%20%5C%5C%20%3D%5Cfrac%7B2%7D%7B4%7D%20gal%20)
Blue paint
![\frac{7}{8}gal](https://tex.z-dn.net/?f=%20%5Cfrac%7B7%7D%7B8%7Dgal%20)
Find the
amount of blue paint left after painting the mural
![(\frac{7}{8} -\frac{3}{4} )=(7-2*3)/8\\ \\ =\frac{1}{8} gal](https://tex.z-dn.net/?f=%20%28%5Cfrac%7B7%7D%7B8%7D%20-%5Cfrac%7B3%7D%7B4%7D%20%29%3D%287-2%2A3%29%2F8%5C%5C%20%5C%5C%20%3D%5Cfrac%7B1%7D%7B8%7D%20gal%20)
Find the
total amount of paint left after painting the mural
![\frac{7}{12} +\frac{2}{4} +\frac{1}{8} =\frac{(2*7+6*2+3*1)}{24} \\ \\ =\frac{29}{24} gal](https://tex.z-dn.net/?f=%20%5Cfrac%7B7%7D%7B12%7D%20%2B%5Cfrac%7B2%7D%7B4%7D%20%2B%5Cfrac%7B1%7D%7B8%7D%20%3D%5Cfrac%7B%282%2A7%2B6%2A2%2B3%2A1%29%7D%7B24%7D%20%5C%5C%20%5C%5C%20%3D%5Cfrac%7B29%7D%7B24%7D%20gal%20)
![\frac{29}{24} =1\frac{5}{24} gal](https://tex.z-dn.net/?f=%20%5Cfrac%7B29%7D%7B24%7D%20%3D1%5Cfrac%7B5%7D%7B24%7D%20gal%20%20)
therefore
the answer is
![1\frac{5}{24} gal](https://tex.z-dn.net/?f=%201%5Cfrac%7B5%7D%7B24%7D%20gal%20)
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