Question

1) Write an equation to show the amount of money the store will receive from the sale of any amount of nails? 2)Write a ratio that shows the amount of money you expect to make from the sale of the hammers to the amount of money you expect to make in all

If it helps, here is the basic info:

Everything in a store is on sale.

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If you want to, please answer the following, too:

Suppose everything is sold except for half of the hammers. How would the ratio of number 2 change? Can you just take half of each number in the ratio from #2 and make a new ratio? Why or why not?

Answer 1

Basically, use algebra. (The answer is too long to put here HAHA :P)

Explanation:

1) Let the number of pounds of nails sold be `x`. Therefore, each pound of nails will be sold at (`$2x)*70%`, which is `$1.40x` per pound.

2) If I read the question correctly, you mean that everything in the store if sold.
Because they have conveniently added everything up, all you have to do is to sum up everything in the last column and put it as a ratio of the final price of the hammers.

`180:(140+800+180+540)`
`=180:1660`
`=9:83`

The additional question would basically be a slight edit to the above working:

`180/2:(140+800+180+540)`
`=90:1660`
`=9:166`

So, no. You cannot take half of each number in the ratio from question 2 and make a new ratio. This is because ratios simplify both numbers by dividing them by their highest common factors and because only 180 was halved and not 1660, the final ratio cannot be halved.

Extra info: If you make a new ratio from halving both 180 and 1660, the final ratio will still remain the same. Do you know why?