Patel squeezed oranges so that his family could have fresh-squeezed juice for breakfast. He squeezed StartFraction 4 over 17 EndFraction cups from the first orange, StartFraction 3 over 10 EndFraction cups from the second orange, StartFraction 9 over 20 EndFraction cups from the third orange, StartFraction 3 over 11 EndFraction cups from the fourth orange, and StartFraction 7 over 15 EndFraction cups from the fifth orange. Patel estimates that he needs 3 cups of orange juice for his family. About how much more orange juice does he need to reach his estimate?
Answers
Answer:
Given:
Patel squeezed oranges so that his family could have fresh-squeezed juice for breakfast. He squeezed StartFraction 4 over 17 EndFraction cups from the first orange, StartFraction 3 over 10 EndFraction cups from the second orange, StartFraction 9 over 20 EndFraction cups from the third orange, StartFraction 3 over 11 EndFraction cups from the fourth orange, and StartFraction 7 over 15 EndFraction cups from the fifth orange.
Patel estimates that he needs 2 cups of orange juice for his family.
To find:
How much more orange juice does he need to reach his estimate?
Solution:
The quantity of orange juice squeezed by Patel from each orange:
1st \: orange \rightarrow \frac{4}{17} \:cups1storange→
17
4
cups
2nd \: orange \rightarrow \frac{3}{10} \:cups2ndorange→
10
3
cups
3rd \: orange \rightarrow \frac{9}{20} \:cups3rdorange→
20
9
cups
4th \: orange \rightarrow \frac{3}{11} \:cups4thorange→
11
3
cups
5th\: orange \rightarrow \frac{7}{15} \:cups5thorange→
15
7
cups
Total cups of orange juice squeezed by Patel is,
= \frac{4}{17} + \frac{3}{10} + \frac{9}{20} + \frac{3}{11} + \frac{7}{15}
17
4
+
10
3
+
20
9
+
11
3
+
15
7
taking L.C.M. of the denominators i.e., L.C.M. of 17, 10, 20, 11 & 15 = 11220
= \frac{2640 \:+ \:3366 \:+\: 5049 \:+\: 3060\: +\: 5236 }{11220}
11220
2640+3366+5049+3060+5236
= \frac{19351}{11220}\:cups
11220
19351
cups
But, Patel needs 2 cups of juice for his family
∴ The quantity of juice he needs to reach his estimate is,
= 2 - \frac{19351}{11220}2−
11220
19351
= \frac{22440 \:-\: 19351}{11220}
11220
22440−19351
= \frac{3089}{11220} \: cups
11220
3089
cups
≈ \bold{0.2753 \:cups}0.2753cups
Now, we will observe the given options:
(1). \frac{1}{6}
6
1
→ 0.167 cups
(2). \frac{5}{6}
6
5
→ 0.833 cups
(3). 1\frac{2}{3}1
3
2
= \frac{5}{3}
3
5
→ 1.67 cups
(4). 1\frac{5}{6} = \frac{11}{6}1
6
5
=
6
11
→ 1.833 cups
Since from all 4 options, the closest to our answer i.e., 0.2753 cups is the first option i.e., \frac{1}{6} \:cups
6
1
cups
Thus, Patel needs about \underline{\bold{\frac{1}{6}\:cups }}
6
1
cups
of orange juice to reach his estimate.