hard math questions please help.?

Question

Rachel divided her fossil collection into three categories: [;ant fossils, insect fossils and other animal fossils. she had eight more plant fossils than animal fossils. The number of insect fossils she has is three less than four times the number of plant fossils she has.

. If ~a~ represents the number of animal fossils rachel has, write an expression for the number of plant fossils she has.

.write an expression for the number of insect fossils rachel has

. tachel has 41 more insect fossils than animal fossils. use this fact, and your expression from the last question to write an equation for this situation.

. solve your equation to find how many fossils rachel has in each category.

Answer 1

Alright, here we go (God you kids really know how to hammer Yahoo! with algebra, or maybe it's yer parents looking out to help you).

Remember, in algebra, everything is relative to something else. Here, we're looking to find the amount of fossils Rachel has by comparing 3 values to each other. In order to do this we have to give each value just that, a numerical algebraic value.

So first, we're comparing animal fossils to plant fossils. Since she has eight more plant fossils than animal fossils we can write this in two ways:
PF = a, AF = a-8; PF = a+8, AF = a.

Later on, we'll be comparing plant fossils to insect fossils so lets keep this simple by using "a" for Plant Fossils.

The reason we're subtracting 8 here is because we have 8 less animal fossils than plant fossils. We could add 8 as well to the PF number, but like I said, we're keeping this simple since we need to compare two values later.

Now, to compare insect fossils to plant fossils, we need to assign another value. Plant fossils have already been determined to equal "a" so Insect fossils will be something OF a.
"Three less than four times the number of plant fossils" will equal 4a-3. 4a = four times the number of plant fossils, and the "-3" equals three less. Tada!

So now, we just put them together:
a + a-8 + 4a-3
and simplify:
6a-11

Next, we have an equation. We're comparing the animal fossils to insect fossils so start by putting them on opposite sides:
a-8 = 4a-3.
The problem says we have 41 more insect fossils than animal fossils, so add 41 to the animal fossil side to counterbalance.
a-8+41 = 4a-3
simplify
a+33=4a-3
and solve
36=3a
12=a
then plug in to find each category
PF: a = 12
AF: a-8= 4
IF: 4a-3 = 45

That's it!

Answer 2

a=p-8
i=4p-3
i-41=a which turns into i-41=p-8 which becomes 4p-3-41=p-8
which solves to get 12
now plug in 12 for p in the i equation
i=4(12) - 3
so now you have 12 plant fossils and 45 insect fossils
now solve for a
you will get 4 animal, 12 plant and 45 insects

Answer 3

plant=p
insect=i
animal=a

a=p-8
i=4p-3
i=a+41

We know that i is equal to both of the above based on the equation. So we can rewrite that like this:
4p-3=a+41
Then, lets get rid of the a so we are only working with one variable. Subsititute the equivalent value of a
4p-3=p-8+41
Then solve for p
3p=36
p=12
Then plug the known value into the other equations.
a=4, i=45, p=12

Answer 4

a = animal fossils
p = plant fossils
i = insect fossils

a+8=p
i=4p-3 ----> i=4(a+8)-3=4a+32-3 ----> i=4a+29

then i=a+41
so a+41=4a+29
3a+12
a=4 ----> i=45 ----> p=12

Answer 5

f= I=8times 15

i am a accountant.. i know