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)
number of blues ---- x
number of reds ----- 238-x
(3/7)x + (5/8)(238-x) = 124
solve for x
(I suggest multiplying each of the 3 terms by 56 , the LCD )
To solve this problem, we can start by setting up an equation. Let's denote the number of blue marbles Timothy had as "B" and the number of red marbles as "R".
According to the problem, Timothy gave away 3/7 of the blue marbles and 5/8 of the red marbles. This can be expressed as:
(3/7)B + (5/8)R = 124
We also know that the total number of marbles Timothy had is 238:
B + R = 238
To solve this system of equations, we can use the method of substitution or elimination. Let's use the substitution method.
We rearrange the second equation to express B in terms of R:
B = 238 - R
Substituting this expression for B in the first equation, we have:
(3/7)(238 - R) + (5/8)R = 124
Now, let's simplify the equation:
(3/7)(238) - (3/7)R + (5/8)R = 124
(714/7) - (3/7)R + (5/8)R = 124
(714/7) + [(5/8) - (3/7)]R = 124
To simplify further, we need to find a common denominator for (5/8) and (3/7):
40 is the least common multiple of 7 and 8. Therefore, we can rewrite (5/8) and (3/7) with the common denominator of 40:
(5/8) = (25/40), and (3/7) = (15/40)
Substituting these values back into the equation, we have:
(714/7) + [(25/40) - (15/40)]R = 124
(714/7) + (10/40)R = 124
Now, let's simplify and solve for R:
(714/7) + (1/4)R = 124
Multiplying both sides by 28 to eliminate the denominators:
4(714) + 7R = 124(28)
2856 + 7R = 3472
Subtracting 2856 from both sides:
7R = 616
Now, divide both sides by 7 to isolate R:
R = 88
Therefore, Timothy gave away 88 red marbles.