John has some marbles. Sally has 5 more than twice as many as John. Ingrid has 4
times as many marbles as John. If the three friends have 96 marbles in all, how many
marbles does each person have? Write an algebraic equation (NO GUESS AND CHECK!)
and solve
s = 2j+5
i = 4j
s+j+i = 96
Now solve, using your method of choice.
S= 35
I= 60
J= 15
vaffanculo
To solve this problem, we can set up three algebraic equations based on the information given.
Let's say John has x marbles.
Based on the given information, Sally has 5 more than twice as many as John, so Sally has (2x + 5) marbles.
Ingrid has 4 times as many marbles as John, so Ingrid has 4x marbles.
The sum of their marbles is 96, so we can add up these equations and set it equal to 96:
x + (2x + 5) + 4x = 96
Now, let's solve this equation:
Combine like terms:
7x + 5 = 96
Subtract 5 from both sides of the equation:
7x = 91
Divide both sides of the equation by 7:
x = 13
So, John has 13 marbles.
Now, we can substitute x = 13 into the equations for Sally and Ingrid:
Sally: 2x + 5 = 2(13) + 5 = 26 + 5 = 31 marbles
Ingrid: 4x = 4(13) = 52 marbles
Therefore, John has 13 marbles, Sally has 31 marbles, and Ingrid has 52 marbles.