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Sagot :
Given:
Lynee bought a bag of grapefruit, [tex]1\dfrac{5}{8}[/tex] pounds of apples, and [tex]2\dfrac{3}{16}[/tex] pounds of bananas.
The total weight of her purchase was [tex]7\dfrac{1}{2}[/tex] pounds.
To find:
The weight of the bag of grapefruit.
Solution:
We have,
Weight of apples = [tex]1\dfrac{5}{8}[/tex] pounds.
Weight of bananas = [tex]2\dfrac{3}{16}[/tex] pounds.
Total weight of her purchase = [tex]7\dfrac{1}{2}[/tex] pounds.
Let x be the weight of the bag of grapefruit.
[tex]x+1\dfrac{5}{8}+2\dfrac{3}{16}=7\dfrac{1}{2}[/tex]
[tex]x+\dfrac{1(8)+5}{8}+\dfrac{2(16)+3}{16}=\dfrac{7(2)+1}{2}[/tex]
[tex]x+\dfrac{13}{8}+\dfrac{35}{16}=\dfrac{15}{2}[/tex]
[tex]\dfrac{16x+26+35}{16}=\dfrac{15}{2}[/tex]
Multiply both sides by 16.
[tex]16x+61=120[/tex]
[tex]16x=120-61[/tex]
[tex]16x=59[/tex]
[tex]x=\dfrac{59}{16}[/tex]
[tex]x=3\dfrac{11}{16}[/tex]
Therefore, the weight of a bag of grapefruit is [tex]3\dfrac{11}{16}[/tex] pounds.
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