Question

Josh has fewer than 80 pens. If he puts them in groups of 7, he will have 5 pens left. If he puts them in groups of 9, he will have 3 pens left. How many pens does David have?

Answer 1

Josh has 75 pens
10*7 + 5 = 75
9*8 + 3 = 75

Answer 2

To solve this problem, we can set up a system of equations.

Let x be the total number of pens Josh has.

We know that x is less than 80, and we can represent the number of pens left when Josh puts them in groups of 7 and 9 as follows:

x = 7a + 5
x = 9b + 3

Where a and b are integers representing the number of groups of 7 and 9 respectively.

We can then solve this system of equations to find the value of x:

7a + 5 = 9b + 3
7a - 9b = -2
7(a - b) = -2
a - b = -2/7

Since a and b are integers, the only possible values for a and b that satisfy this equation are a = 5 and b = 3.

Plugging these back into the equations above, we find that:
x = 7(5) + 5 = 40

Therefore, Josh has 40 pens.

Answer 3

Apologies for the error in my previous response. Thank you for providing the correct solution.

Josh has 75 pens, which can be grouped as follows:
- 10 groups of 7 pens with 5 pens left over (10 * 7 + 5 = 75)
- 8 groups of 9 pens with 3 pens left over (8 * 9 + 3 = 75)

Therefore, David has 75 pens. Thank you for the correction.