QuestionZach's first quiz score is what if his last score is $30$ less than $2$ times his first, and their sum is $150$ ?

Studdy Solution

STEP 1

Assumptions1. Zach's last quiz score was30 points less than twice his first score. . The sum of his two scores is150.

STEP 2

Let's denote Zach's first quiz score as $x$ . According to the problem, his last quiz score is30 points less than twice his first score, so we can express his last score as $2x -30$ .

STEP 3

We know that the sum of his two scores is150, so we can set up the following equation $x +2x -30 =150$

STEP 4

implify the equation by combining like terms.
$3x -30 =150$

STEP 5

Add30 to both sides of the equation to isolate the term with $x$ .
$3x =150 +30$

STEP 6

Calculate the right side of the equation.
$3x =180$

STEP 7

Divide both sides of the equation by3 to solve for $x$ .
$x =180 /3$

STEP 8

Calculate the value of $x$ .
$x =60$ Zach's first quiz score was60 points.

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QuestionZach's first quiz score is what if his last score is $30$ less than $2$ times his first, and their sum is $150$ ?

Studdy Solution

STEP 1

Assumptions1. Zach's last quiz score was30 points less than twice his first score. . The sum of his two scores is150.

STEP 2

Let's denote Zach's first quiz score as $x$ . According to the problem, his last quiz score is30 points less than twice his first score, so we can express his last score as $2x -30$ .

STEP 3

We know that the sum of his two scores is150, so we can set up the following equation $x +2x -30 =150$

STEP 4

implify the equation by combining like terms.
$3x -30 =150$

STEP 5

Add30 to both sides of the equation to isolate the term with $x$ .
$3x =150 +30$

STEP 6

Calculate the right side of the equation.
$3x =180$

STEP 7

Divide both sides of the equation by3 to solve for $x$ .
$x =180 /3$

STEP 8

Calculate the value of $x$ .
$x =60$ Zach's first quiz score was60 points.

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QuestionZach's first quiz score is what if his last score is 303030 less than 222 times his first, and their sum is 150150150?

Studdy Solution

STEP 1

Assumptions1. Zach's last quiz score was30 points less than twice his first score. . The sum of his two scores is150.

STEP 2

Let's denote Zach's first quiz score as xxx. According to the problem, his last quiz score is30 points less than twice his first score, so we can express his last score as 2x−302x -302x−30.

STEP 3

We know that the sum of his two scores is150, so we can set up the following equationx+2x−30=150x +2x -30 =150x+2x−30=150

STEP 4

implify the equation by combining like terms.3x−30=1503x -30 =1503x−30=150

STEP 5

Add30 to both sides of the equation to isolate the term with xxx.3x=150+303x =150 +303x=150+30

STEP 6

Calculate the right side of the equation.3x=1803x =1803x=180

STEP 7

Divide both sides of the equation by3 to solve for xxx.x=180/3x =180 /3x=180/3

STEP 8

Calculate the value of xxx.x=60x =60x=60Zach's first quiz score was60 points.

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QuestionZach's first quiz score is what if his last score is $30$ less than $2$ times his first, and their sum is $150$ ?

Let's denote Zach's first quiz score as $x$ . According to the problem, his last quiz score is30 points less than twice his first score, so we can express his last score as $2x -30$ .

We know that the sum of his two scores is150, so we can set up the following equation $x +2x -30 =150$

implify the equation by combining like terms.
$3x -30 =150$

Add30 to both sides of the equation to isolate the term with $x$ .
$3x =150 +30$

Calculate the right side of the equation.
$3x =180$

Divide both sides of the equation by3 to solve for $x$ .
$x =180 /3$

Calculate the value of $x$ .
$x =60$ Zach's first quiz score was60 points.