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a textbook store sold a combined total of 340 history and sociology textbooks in a week. the number of history textbooks sold was three times the number of sociology textbooks sold. how many textbooks of each type were sold?

Respuesta :

Answer:

85 sociology books

255 history books

Step-by-step explanation:

h = history textbooks

s = sociology textbooks

h + s = 340

h = 3s

3s + s = 340

4s = 340

s = 85

h = 3s = 3(85) = 255

semsee45

Answer:

255 history textbooks

85 sociology textbooks

Step-by-step explanation:

Define the variables:

  • Let x be the number of history textbooks sold.
  • Let y be the number of sociology textbooks sold.

Given information:

  • Total number of textbooks sold in a week was 340.
  • The number of history textbooks sold was three times the number of sociology textbooks sold.

Create a system of equations with the given information and defined variables:

[tex]\begin{cases}x+y=340\\\;\;\;\:\:\:\:x=3y\end{aligned}[/tex]

Substitute the second equation into the first equation and solve for y:

[tex]\implies 3y+y=340[/tex]

[tex]\implies 4y=340[/tex]

[tex]\implies y=340 \div 4[/tex]

[tex]\implies y=85[/tex]

Substitute the found value of y into the second equation and solve x:

[tex]\implies x=3 \times 85[/tex]

[tex]\implies x=255[/tex]

Therefore, the number of each type of textbooks sold were:

  • 255 history textbooks.
  • 85 sociology textbooks.

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