the number of pages is a 2-digit number. the number of photos on a page is a 1- digit number. the number of pages is 60 more than the number of photos on a page. the number of pages is divided by the number of photos on a page is 16. What is the number of pages?????????
To solve this problem, we can break it down into steps:
Step 1: Represent the unknowns.
Let's assign the number of pages as 'P' and the number of photos per page as 'N'.
Step 2: Translate the given information into equations.
According to the problem:
- The number of pages is a 2-digit number, so P is between 10 and 99.
- The number of photos on a page is a 1-digit number, so N is between 1 and 9.
- The number of pages is 60 more than the number of photos per page: P = N + 60.
- The number of pages divided by the number of photos on a page is 16: P/N = 16.
Step 3: Substitute the value of P from the second equation into the fourth equation.
Substituting P = N + 60 into the equation P/N = 16:
(N + 60)/N = 16.
Step 4: Solve the equation.
We can solve the equation by cross-multiplying:
N + 60 = 16N.
Simplifying this equation:
60 = 15N.
Dividing both sides of the equation by 15:
N = 60/15,
N = 4.
Step 5: Substitute the value of N back into the second equation to find P.
P = N + 60,
P = 4 + 60,
P = 64.
Therefore, the number of pages is 64.