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 )
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 )
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.