In June, Katherine bought 21 cans of food and 3 bags of litter for a total of $42. In July she spent $60 on 32 cans of food and 4 bags of litter. What is the cost of one bag of litter? answer please!

Question

anonymous · Answer

You need to set this up as 2 equations with variables for the 2 unknowns -- you don't know the cost of one bag of litter or the cost of 1 can of food.

So, you could set up one equation for June:
(21 cans) * (can price) + (3 bags of litter) * (litter price) = 42 dollars

but use variables to make it neater... let "can price" be C and "litter price" be L

so 21C + 3L = 42

Can you set up the July equation?

anonymous · Answer

I cant, I have so much trouble with word problems.
:(

anonymous · Answer

how much did she spend on food in July?  It's the number of cans of food multiplied by the price of a can of food, right?

anonymous · Answer

so she bought 32 cans of food, and she must have spent 32 x C, since C is the price of 1 can.

anonymous · Answer

you just need to translate the words into math sentences like I'm showing you...
If she bought 32 cans of food in July, then she spent 32C on food.

If she also bought 4 bags of litter, she spend 4L on litter.

All together for July, she spent 32C + 4L, and the problem says she spent $60 total in July, so 32C + 4L = 60

anonymous · Answer

now what do i do

anonymous · Answer

now you have 2 equations and 2 unknowns...

Equation 1:  21C + 3L = 42
Equation 2:  32C + 4L = 60

You can solve it through substitution or elimination or a bit of both.

anonymous · Answer

To make the numbers easier, you might also notice that you can divide the whole first equation through by 3... everything in it is a multiple of 3.  And everything in Equation 2 is a multiple of 4, so divide that through by 4.

Equation 1: 21C + 3L = 42   --->>> 7C + L = 14
Equation 2: 32C + 4L = 60   --->>> 8C + L = 15

anonymous · Answer

could you solve it by elimination? I need to see the steps because elimination gets confusing

anonymous · Answer

wait...is the answer $7?

anonymous · Answer

I think it is easier to solve by elimination after you simplify both equations like I just showed...

Using those modified equations, subtract the first from the second...

    { Equation 2:  8C + L = 15 }
-  { Equation 1:  7C + L = 14 }
---------------------------
            8C - 7C + L - L = 15 - 14

Can you simplify that expression?

anonymous · Answer

I have the answer now:) thank you for your help! I have to leave now. Bye!

anonymous · Answer

Good luck :)  Glad to help :)