Greg's number of pencils is 3/5 the number of Tom's pencils. Together they have 56 pencils.How many pencils does Greg have? How many pencils does Tom have? How many more pencils does Tom have than Greg?
Let Tom's pencil = x
Greg's = 3/5(x)
Totals = 3/5(x) x = 56
= 3x/5 x = 56
= 3x 5x = 280
= 8x/8 = 280/8
= X = 35
Therefore. Tom's pencil = 35
Greg's = 3/5(35) = 21
Tom has (35 - 21) = 14 pencils more than greg.
Let G=Greg's pencils & T=Tom's penils.
G + T = 56
G = 56 - T
G = (3/5)T
(3/5)T = 56 - T
(3/5)T + T = 56
(8/5)T = 56
T = 56*(5/8) = (56/8)*5 = 7*5 = 35
G = (3/5)*35 = 3*7 = 21
35 + 21 = 56
To solve this problem, let's set up a system of equations.
Let G represent the number of pencils Greg has, and let T represent the number of pencils Tom has.
From the given information, we know that Greg's number of pencils is 3/5 the number of Tom's pencils:
G = (3/5)T
We also know that together they have 56 pencils:
G + T = 56
To find the values of G and T, we can use substitution or elimination.
Method 1: Substitution
Substitute the value of G from the first equation into the second equation:
(3/5)T + T = 56
Multiply both sides of the equation by 5 to remove the fraction:
3T + 5T = 280
Combine like terms:
8T = 280
Divide both sides of the equation by 8:
T = 35
Now substitute the value of T back into the first equation to find G:
G = (3/5) * 35
G = 21
So, Greg has 21 pencils and Tom has 35 pencils.
Method 2: Elimination
Multiply the first equation by 5 to make the coefficients of G and T equal in both equations:
5G = 3T
Now we have the two equations:
5G = 3T
G + T = 56
Multiply the second equation by -3 to create opposite coefficients for T:
-3G - 3T = -168
Now, add the two equations together:
5G + (-3G) + 3T + (-3T) = 3T + (-3T) + 56 + (-168)
Simplifying the equation:
2G = -112
Divide both sides of the equation by 2:
G = -56
This solution doesn't make sense in the context of the problem since the number of pencils cannot be negative. Therefore, we discard this solution.
Hence, Greg has 21 pencils, Tom has 35 pencils, and Tom has 14 more pencils than Greg.