word problem see below

Question

A textbook store sold a combined total of 308 history and math textbooks in a week. The number of history textbooks sold was three times the number of math textbooks sold. How many textbooks of each type were sold?

Answer 1

For this type of problem, we set up a system of equations.

 

m = number of math textbooks

h = number of history textbooks

 

Since the total number of books is 308, it follows that:

 

m + h = 308

 

Then, the number of history books is 3 times the number of math books. Therefore:

 

h = 3m

 

Now, we use substitution. Because h = 3m, we can substitute the h in the original equation for 3m. Therefore:

 

m + 3m = 308

 

...combine like terms...

 

4m = 308

 

Divide by 4:

 

m = 77

 

So there are 77 math textbooks. How many history books does that leave? 

 

We can use either equation:

 

77 + h = 308

Subtract 77...

h = 231

 

OR the other equation:

h = 3(77)

h = 231

 

Final answer:

 

77 math books, 231 history books.

 

 

 

Answer 2

For this type of problem, you can write a system of equations. Let x = number of history textbooks sold and let y = number of math textbooks sold. Then:

 

x + y = 308    (there were 308 total textbooks sold)

x = 3y    (the number of history textbooks sold was three times the number of math textbooks sold)

 

 

Plug x = 3y into the first equation and solve for y:

 

3y + y = 308

4y = 308

y = 77

 

 

Now, plug y = 77 back into the second equation and solve for x:

 

x = 3(77)

x = 231

 

 

There were 231 history textbooks sold and 77 math textbooks sold.