Question Find the number of psychology and history textbooks sold, given that the total sold was 290 and the number of psychology textbooks was 42 more than the number of history textbooks. Let $x$ be the number of history textbooks sold. Then the number of psychology textbooks sold is $x + 42$ . The total number of textbooks sold is $x + (x + 42) = 290$ . Solve for $x$ to find the number of textbooks of each type sold.

Studdy Solution

STEP 1

Assumptions
1. The combined total of psychology and history textbooks sold is 290.
2. The number of psychology textbooks sold is 42 more than the number of history textbooks sold.

STEP 2

Let's denote the number of history textbooks sold as $H$ .

STEP 3

Since the number of psychology textbooks sold is 42 more than the number of history textbooks sold, we can denote the number of psychology textbooks sold as $H + 42$ .

STEP 4

Now we can set up an equation based on the total number of textbooks sold.
$H + (H + 42) = 290$

STEP 5

Combine like terms to simplify the equation.
$2H + 42 = 290$

STEP 6

Subtract 42 from both sides of the equation to isolate the terms with $H$ .
$2H = 290 - 42$

STEP 7

Calculate the right side of the equation.
$2H = 248$

STEP 8

Divide both sides of the equation by 2 to solve for $H$ .
$H = \frac{248}{2}$

STEP 9

Calculate the value of $H$ .
$H = 124$

STEP 10

Now that we have the number of history textbooks sold, we can find the number of psychology textbooks sold by adding 42 to $H$ .
$Psychology\, textbooks = H + 42$

STEP 11

Plug in the value of $H$ to find the number of psychology textbooks sold.
$Psychology\, textbooks = 124 + 42$

STEP 12

Calculate the number of psychology textbooks sold.
$Psychology\, textbooks = 166$
Number of psychology textbooks sold: 166 Number of history textbooks sold: 124

Was this helpful?

Studdy Solution

STEP 1

Assumptions
1. The combined total of psychology and history textbooks sold is 290.
2. The number of psychology textbooks sold is 42 more than the number of history textbooks sold.

STEP 2

Let's denote the number of history textbooks sold as $H$ .

STEP 3

Since the number of psychology textbooks sold is 42 more than the number of history textbooks sold, we can denote the number of psychology textbooks sold as $H + 42$ .

STEP 4

Now we can set up an equation based on the total number of textbooks sold.
$H + (H + 42) = 290$

STEP 5

Combine like terms to simplify the equation.
$2H + 42 = 290$

STEP 6

Subtract 42 from both sides of the equation to isolate the terms with $H$ .
$2H = 290 - 42$

STEP 7

Calculate the right side of the equation.
$2H = 248$

STEP 8

Divide both sides of the equation by 2 to solve for $H$ .
$H = \frac{248}{2}$

STEP 9

Calculate the value of $H$ .
$H = 124$

STEP 10

Now that we have the number of history textbooks sold, we can find the number of psychology textbooks sold by adding 42 to $H$ .
$Psychology\, textbooks = H + 42$

STEP 11

Plug in the value of $H$ to find the number of psychology textbooks sold.
$Psychology\, textbooks = 124 + 42$

STEP 12

Calculate the number of psychology textbooks sold.
$Psychology\, textbooks = 166$
Number of psychology textbooks sold: 166 Number of history textbooks sold: 124

Get Studdy

Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Studdy Solution

STEP 1

Assumptions1. The combined total of psychology and history textbooks sold is 290.2. The number of psychology textbooks sold is 42 more than the number of history textbooks sold.

STEP 2

Let's denote the number of history textbooks sold as HHH.

STEP 3

Since the number of psychology textbooks sold is 42 more than the number of history textbooks sold, we can denote the number of psychology textbooks sold as H+42H + 42H+42.

STEP 4

Now we can set up an equation based on the total number of textbooks sold.H+(H+42)=290H + (H + 42) = 290H+(H+42)=290

STEP 5

Combine like terms to simplify the equation.2H+42=2902H + 42 = 2902H+42=290

STEP 6

Subtract 42 from both sides of the equation to isolate the terms with HHH.2H=290−422H = 290 - 422H=290−42

STEP 7

Calculate the right side of the equation.2H=2482H = 2482H=248

STEP 8

Divide both sides of the equation by 2 to solve for HHH.H=2482H = \frac{248}{2}H=2248​

STEP 9

Calculate the value of HHH.H=124H = 124H=124

STEP 10

Now that we have the number of history textbooks sold, we can find the number of psychology textbooks sold by adding 42 to HHH.Psychology textbooks=H+42Psychology\, textbooks = H + 42Psychologytextbooks=H+42

STEP 11

Plug in the value of HHH to find the number of psychology textbooks sold.Psychology textbooks=124+42Psychology\, textbooks = 124 + 42Psychologytextbooks=124+42

STEP 12

Calculate the number of psychology textbooks sold.Psychology textbooks=166Psychology\, textbooks = 166Psychologytextbooks=166Number of psychology textbooks sold: 166 Number of history textbooks sold: 124

Get Studdy

Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Assumptions
1. The combined total of psychology and history textbooks sold is 290.
2. The number of psychology textbooks sold is 42 more than the number of history textbooks sold.

Let's denote the number of history textbooks sold as $H$ .

Since the number of psychology textbooks sold is 42 more than the number of history textbooks sold, we can denote the number of psychology textbooks sold as $H + 42$ .

Now we can set up an equation based on the total number of textbooks sold.
$H + (H + 42) = 290$

Combine like terms to simplify the equation.
$2H + 42 = 290$

Subtract 42 from both sides of the equation to isolate the terms with $H$ .
$2H = 290 - 42$

Calculate the right side of the equation.
$2H = 248$

Divide both sides of the equation by 2 to solve for $H$ .
$H = \frac{248}{2}$

Calculate the value of $H$ .
$H = 124$

Now that we have the number of history textbooks sold, we can find the number of psychology textbooks sold by adding 42 to $H$ .
$Psychology\, textbooks = H + 42$

Plug in the value of $H$ to find the number of psychology textbooks sold.
$Psychology\, textbooks = 124 + 42$

Calculate the number of psychology textbooks sold.
$Psychology\, textbooks = 166$
Number of psychology textbooks sold: 166 Number of history textbooks sold: 124