Redda wanted to give marbles to the neighborhood children. If he gives 10 marbles to each child, he would be 35 short. If he tries 13 marbles each, he will would be short of 119 marbles. How many marbles does he have in total?

Question

Redda wanted to give marbles to the neighborhood children. If he gives 10 marbles to each child,  he would be 35 short. If he tries 13 marbles each, he  will would be short of 119 marbles. How many marbles does he have in total?

Genesis Amaya · Accepted Answer

245

Let x be the number of children, and y be the total number of marbles he has. For the first statement, the equation will be: #10x = y + 35# For the second statement, the equation will be: #13x = y + 119# Make y the subject of the first equation. #y = 10x - 35# Substitute this equation into the second equation #13x = (10x - 35) + 119# #3x=84# #x=28# Substitute x into the the first equation to get y. #10(28) = y +35# #y = 245#

Jeremiah Andrews · Answer

undefined Let's denote the total number of children in the neighborhood as $ n $. According to the problem:

1. If Redda gives 10 marbles to each child, he would be 35 marbles short:
   $$ 10n = T - 35 $$

2. If Redda gives 13 marbles to each child, he would be 119 marbles short:
   $$ 13n = T - 119 $$

Where $ T $ represents the total number of marbles Redda has.

We can solve these equations simultaneously to find the values of $ n $ and $ T $. Subtracting the first equation from the second, we get:
$$ 3n = 84 $$
$$ n = 28 $$

Substituting the value of $ n $ into either equation, we can find $ T $:
$$ 10(28) = T - 35 $$
$$ T = 280 + 35 $$
$$ T = 315 $$

So, Redda has a total of 315 marbles.