Lynne bought a bag of grapefruit 1 5 8 ponds of apples and 2 3 16pounds of bananas The total weight of her purchase was 7½ pounds How many pounds was the grapefruit?

Let the weight of the grapefruit be ( x ) pounds. According to the information given, the total weight of the fruits can be expressed as:

[ x + 1\frac{5}{8} + 2\frac{3}{16} = 7\frac{1}{2} ]

First, convert all mixed numbers to improper fractions:

• ( 1\frac{5}{8} = \frac{13}{8} )
• ( 2\frac{3}{16} = \frac{35}{16} )
• ( 7\frac{1}{2} = \frac{15}{2} )

Now, convert ( \frac{15}{2} ) to a common denominator with the other fractions, which is 16:

[ \frac{15}{2} = \frac{120}{16} ]

Now, we can rewrite the equation:

[ x + \frac{13}{8} + \frac{35}{16} = \frac{120}{16} ]

Convert ( \frac{13}{8} ) to sixteenths:

[ \frac{13}{8} = \frac{26}{16} ]

Combine the fractions:

[ x + \frac{26}{16} + \frac{35}{16} = \frac{120}{16} ]

This simplifies to:

[ x + \frac{61}{16} = \frac{120}{16} ]

Subtract ( \frac{61}{16} ) from both sides:

[ x = \frac{120}{16} - \frac{61}{16} = \frac{59}{16} ]

Thus, the weight of the grapefruit is ( \frac{59}{16} ) pounds, which is approximately 3.69 pounds.