Timothy had a total of 238 blue and red marbles. He gave 3/7 of the blue marbles and 5/8 of the red marbles away. Altogether, Timothy gave away 124 marbles.How many red marbles did Timothy give away? (Skill: Equations)
B + R = 238
3B/7 + 5R/8 = 124
Multiply both sides of the last equation by 8/5.
24B/35 + R = 198.4
Subtract the above equation from the first one.
11B/35 = 39.6
Multiply both sides by 35/11
B = 126
R = 112 is the number of red marbles.
654
87
567
To solve this problem, we can set up an equation based on the given information.
Let's call the number of blue marbles Timothy had initially B, and the number of red marbles R.
According to the problem, Timothy gave away 3/7 of the blue marbles, which means he gave away (3/7)B blue marbles.
Timothy also gave away 5/8 of the red marbles, which means he gave away (5/8)R red marbles.
Altogether, Timothy gave away 124 marbles, so we can write the equation:
(3/7)B + (5/8)R = 124 (Equation 1)
We also know that the total number of marbles Timothy had initially is 238, so we can write a second equation:
B + R = 238 (Equation 2)
Now we have a system of two equations with two variables. We can solve this system to find the value of R, which represents the number of red marbles Timothy gave away.
To solve the system, we can use a method like substitution or elimination. Let's use the elimination method here:
First, let's multiply Equation 1 by 56 to eliminate the fractions:
56 * ((3/7)B + (5/8)R) = 56 * 124
Simplifying, we get:
24B + 35R = 6944 (Equation 3)
Now we can subtract Equation 2 from Equation 3 to eliminate B:
(24B + 35R) - (B + R) = 6944 - 238
Simplifying, we get:
23B + 34R = 6706 (Equation 4)
Now we have a new equation with only one variable, R. We can solve this equation to find the value of R:
23B + 34R = 6706
To solve for R, isolate the variable:
34R = 6706 - 23B
Divide both sides by 34:
R = (6706 - 23B) / 34
Now that we have an expression for R in terms of B, we can substitute this expression into Equation 2:
B + (6706 - 23B) / 34 = 238
Multiply both sides by 34 to eliminate the fraction:
34B + 6706 - 23B = 34 * 238
Simplifying, we get:
11B + 6706 = 8092
Subtract 6706 from both sides to isolate B:
11B = 8092 - 6706
Calculating, we get:
11B = 1386
Divide both sides by 11 to solve for B:
B = 1386 / 11
B = 126
Now, substitute the value of B back into Equation 2 to find R:
126 + R = 238
Subtract 126 from both sides:
R = 238 - 126
R = 112
Therefore, Timothy gave away 112 red marbles.