21. \( \frac{2}{3} \) the sum of two numbers is 12 . One of the numbers is 10 , what is the other number? Answer. \( \qquad \) 22. Rambo has 8 red, 12 green, 6 blue and 4 white marbles. What FRACTION of his marbles is BLUE? Answer. \( \qquad \) Calculate the sum of \( 1 \frac{3}{4} \) and \( \frac{2}{3} \). Answer. \( \qquad \)

To find the other number, let's denote the unknown number as \( x \). The problem states that \( \frac{2}{3} \) of the sum of the two numbers is equal to 12. We can write the equation as follows: \[ \frac{2}{3}(x + 10) = 12 \] Now, we multiply both sides by the reciprocal of \( \frac{2}{3} \), which is \( \frac{3}{2} \): \[ x + 10 = 12 \times \frac{3}{2} \] Calculating the right side gives us: \[ x + 10 = 18 \] Subtracting 10 from both sides results in: \[ x = 8 \] So, the other number is \( \boxed{8} \). --- Rambo's collection of marbles includes 8 red, 12 green, 6 blue, and 4 white marbles. To determine the fraction of his marbles that is blue, we first calculate the total number of marbles: \[ 8 + 12 + 6 + 4 = 30 \] Next, we form a fraction with the number of blue marbles as the numerator: \[ \text{Fraction of blue marbles} = \frac{6}{30} \] By simplifying this fraction, we find: \[ \frac{6}{30} = \frac{1}{5} \] Therefore, the fraction of Rambo’s marbles that is blue is \( \boxed{\frac{1}{5}} \). --- To calculate the sum of \( 1 \frac{3}{4} \) and \( \frac{2}{3} \), let's first convert \( 1 \frac{3}{4} \) into an improper fraction: \[ 1 \frac{3}{4} = \frac{4 \times 1 + 3}{4} = \frac{7}{4} \] Now, we need to add \( \frac{7}{4} \) and \( \frac{2}{3} \). To do so, we need a common denominator, which is 12: Converting \( \frac{7}{4} \) gives: \[ \frac{7}{4} = \frac{7 \times 3}{4 \times 3} = \frac{21}{12} \] And converting \( \frac{2}{3} \): \[ \frac{2}{3} = \frac{2 \times 4}{3 \times 4} = \frac{8}{12} \] Now we can add the two fractions: \[ \frac{21}{12} + \frac{8}{12} = \frac{29}{12} \] Thus, the sum of \( 1 \frac{3}{4} \) and \( \frac{2}{3} \) is \( \boxed{\frac{29}{12}} \).