Probability Word Problems

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Question 1 of 1

Lisa guessed the number of marbles in a jar, but guessed

35

$35$ too many. Her friend Gemma guessed

15

$15$ too few. The average of both guesses was

180

$180$ . How many marbles are in the jar?

(170)

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A word problem can be translated into an equation for easier solving.

First, represent the components of the problem

number of marbles:

x

$x$

Lisa’s guess:

x + 35

$x+35$

Gemma’s guess:

x - 15

$x-15$

Translate the problem into an equation using the representations above

Remember that to find the average of a number, get their sum and divide it by

2

$2$

The average of the $2$ $2$ guesses	is	$180$ $180$
$\frac{(x + 35) + (x - 15)}{2}$ $((x+35)+(x-15))/2$	$=$ $=$	$180$ $180$

Solve for

x

$x$

$\frac{(x + 35) + (x - 15)}{2}$ $((x+35)+(x-15))/2$	$=$ $=$	$180$ $180$

$\frac{(x + 35) + (x - 15)}{2}$ $((x+35)+(x-15))/2$ $\times 2$ $times2$	$=$ $=$	$180$ $180$ $\times 2$ $times2$	Multiply both sides to $2$ $2$

$(x + 35) + (x - 15)$ $(x+35)+(x-15)$	$=$ $=$	$360$ $360$
$2 x + 20$ $2x+20$	$=$ $=$	$360$ $360$
$2 x + 20$ $2x+20$ $- 20$ $-20$	$=$ $=$	$360$ $360$ $- 20$ $-20$	Subtract $20$ $20$ from both sides
$2 x$ $2x$	$=$ $=$	$340$ $340$
$2 x$ $2x$ $\div 2$ $-:2$	$=$ $=$	$340$ $340$ $\div 2$ $-:2$	Divide both sides by $2$ $2$
$x$ $x$	$=$ $=$	$170$ $170$

170

$170$

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