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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?
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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
( x + 35 ) + ( x − 15 ) 2 ( x + 35 ) + ( x - 15 ) 2
= =
180 180
( x + 35 ) + ( x − 15 ) 2 ( x + 35 ) + ( x - 15 ) 2
= =
180 180
( x + 35 ) + ( x − 15 ) 2 ( x + 35 ) + ( x - 15 ) 2 × 2 × 2
= =
180 180 × 2 × 2
Multiply both sides to 2 2
( x + 35 ) + ( x − 15 ) ( x + 35 ) + ( x - 15 )
= =
360 360
2 x + 20 2 x + 20
= =
360 360
2 x + 20 2 x + 20 − 20 - 20
= =
360 360 − 20 - 20
Subtract 20 20 from both sides
2 x 2 x
= =
340 340
2 x 2 x ÷ 2 ÷ 2
= =
340 340 ÷ 2 ÷ 2
Divide both sides by 2 2
x x
= =
170 170