joseph had 5 time as many marble as alex at first, joseph gave alex 42 marbles, alex had many marble as joseph, how many marble did alex and joseph altogether?
j = 5a
j-42 = a+42
now solve for a and j.
To calculate the number of marbles Joseph and Alex have altogether, we need to break down the information given step by step.
Let's start with the information provided: Joseph initially had 5 times as many marbles as Alex.
Let's say the number of marbles Alex had at first is "x."
According to the given information, Joseph had 5 times as many marbles as Alex, so Joseph had 5*x marbles initially.
Now, Joseph gave 42 marbles to Alex. After this, Alex has 42+x marbles, and Joseph has 5*x - 42 marbles left.
Next, we are given that Alex has as many marbles as Joseph. So we can set up an equation to represent this:
42 + x = 5*x - 42
To solve for x, let's simplify the equation.
42 = 5*x - 42 + x
42 = 6*x - 42
Now, by adding 42 to both sides of the equation, we get:
42 + 42 = 6*x
Simplifying further:
84 = 6*x
To solve for x, we divide both sides by 6:
84/6 = x
14 = x
Therefore, Alex initially had 14 marbles.
To calculate how many marbles Joseph initially had, we need to multiply Alex's initial amount by 5:
Joseph initially had 5 * 14 = 70 marbles.
Finally, to find the total number of marbles Joseph and Alex have altogether, we add their final amounts:
Joseph has 5*14 - 42 = 28 marbles left after giving 42 to Alex.
So, the total number of marbles Alex and Joseph have altogether is:
70 + 28 = 98 marbles.