3/4 of Ali’s marbles is equal to 5/6 of John’s marbles. If Ali has 76 more marbles than John, what is the total number of marbles Ali and John have altogether?
3/4 a = 5/6 j
a = j+76
Now solve for a and j, and then find a+j
Let's assume the number of John's marbles to be x.
According to the given information, 3/4 of Ali's marbles is equal to 5/6 of John's marbles.
So we can write the equation as:
(3/4) * Ali's marbles = (5/6) * John's marbles
Since Ali has 76 more marbles than John, we can write another equation as:
Ali's marbles = John's marbles + 76
Now, let's solve these equations step-by-step to find the values of Ali's and John's marbles.
From the second equation:
Ali's marbles = x + 76
Substitute this value in the first equation:
(3/4) * (x + 76) = (5/6) * x
Multiply through by 4 and 6 to get rid of the fractions:
3(x + 76) = 5(2x)
Expand:
3x + 228 = 10x
Subtract 3x from both sides:
7x + 228 = 0
Subtract 228 from both sides:
7x = -228
Divide by 7:
x = -228/7
Since the number of marbles cannot be negative, this solution is invalid.
Therefore, there must be an error in the problem statement. Please double-check the information given.
To solve this problem, we can set up an equation:
Let x be the number of John's marbles.
Then, 3/4 of Ali's marbles is equal to 5/6 of John's marbles:
(3/4) * Ali's marbles = (5/6) * John's marbles
Next, we know that Ali has 76 more marbles than John:
Ali's marbles = John's marbles + 76
Now, we can substitute the value of Ali's marbles from the second equation into the first equation:
(3/4) * (John's marbles + 76) = (5/6) * John's marbles
To get rid of the fractions, we can multiply both sides by the least common multiple of 4 and 6, which is 12:
12 * (3/4) * (John's marbles + 76) = 12 * (5/6) * John's marbles
9 * (John's marbles + 76) = 10 * John's marbles
Distributing and simplifying:
9 * John's marbles + 9 * 76 = 10 * John's marbles
9 * John's marbles + 684 = 10 * John's marbles
Subtracting 9 * John's marbles from both sides:
684 = John's marbles
Now, we can find the number of Ali's marbles by substituting this value back into Ali's marbles = John's marbles + 76:
Ali's marbles = 684 + 76 = 760
Finally, to find the total number of marbles Ali and John have altogether, we add their marbles:
Total = Ali's marbles + John's marbles = 760 + 684 = 1444
Therefore, Ali and John have a total of 1444 marbles altogether.