Solve for Weight Distribution: Finding Orange Quantities in Two Boxes with 61½ kg Total

To solve this problem, follow these steps:

• Define the variables: Let $x$ be the weight of oranges in the blue box.

• Set up the equation: Since the red box has 5 kg more than the blue box, its weight is $x + 5$. The total weight of the two boxes is given as $61 \frac{1}{2}$ kg. Thus, the equation is:

$x + (x + 5) = 61 \frac{1}{2}$

Now, simplify and solve the equation step by step:

• Combine like terms: $2x + 5 = 61 \frac{1}{2}$

• Convert the mixed number to an improper fraction for easier calculations: $61 \frac{1}{2} = \frac{123}{2}$

• Write the equation with the fraction: $2x + 5 = \frac{123}{2}$

• Subtract 5 from both sides: $2x = \frac{123}{2} - 5$

• Convert 5 to a fraction with the same denominator: $5 = \frac{10}{2}$

• Subtract the fractions: $2x = \frac{123}{2} - \frac{10}{2} = \frac{113}{2}$

• Divide both sides by 2 to solve for $x$: $x = \frac{113}{2} \div 2 = \frac{113}{4}$

Thus, the weight of oranges in the blue box is $x = \frac{113}{4} = 28 \frac{1}{4}$ kg.

The red box's oranges weigh $x + 5 = \frac{113}{4} + \frac{20}{4} = \frac{133}{4} = 33 \frac{1}{4}$ kg.

Therefore, the solution is:

^{blue box $28\frac{1}{4}$ red box $33\frac{1}{4}$}