Could you help me on number 4 of page 69 please? I forgot how to set up the equation

Sure. Here’s the question:

To write the equations, let’s say that *c* is the number of campers. The question gives us *n* for the number of lollipops.

“…if she were to give each camper 7 lollipops, she would have 10 left over”

That’s straightforward enough: if she would have 10 lollipops left over, then the number of lollipops must be 10 more than the product of 7 and the number of campers.

*n* = 7*c* + 10

“…if she eats one of the lollipops herself, she can give each camper 8 lollipops and have none left over”

This is a bit tricky because of her eating one, but the best way to think of that is that the number of lollipops she has is 1 greater than the product of 8 and the number of campers.

*n* = 8*c* + 1

Once we have the equations, all we need to do is solve for *c*. Let’s do that by elimination:

* n* = 8*c* + 1

– (*n* = 7*c* + 10)

0 = *c* – 9

9 = *c*

When you’re setting up question 4 of page 69, why aren’t you subtracting 1? Since she’s eating the lollipop, doesn’t it mean that it’s going away?

Good question. Sure, that’s another way of looking at it. In that case, though, you’d subtract 1 from the left side of the equation, like so: n – 1 = 8c. 1 lollipop goes away and then there are exactly 8 for each camper. Looking back I realize that that’s how I actually set it up in my solution in the book. 🙂

The way I have it above, I’m saying that the number of lollipops is 8 for each camper and then 1 more, which Bethany can eat. I went that way because then each equation is in the same n= form.

Of course, the two equations are equivalent, so whichever makes more intuitive sense to you is fine.