how do i write the equations so i can solve it i will do the solving but help me out with the equation please.for the following:

Four pencils and five pens cost$2.00. THree pencils and four pens cost $1.58. Find the cost fo a pencil and the cost of a pen.

and then also for this one:

Together, a stakeboard and a bicycle cost $199.00. THe skateboard cost $51.00 less than the bicycle. How much does each cost.

Ok..Number 1

let P represent the pencils and N represent the pens

So

4P + 5N = 2.00
3P + 4N = 1.58

nUMBER 2

let x represent the cost of the bicycle

so
The equation is

x + x - 51= 199

Hope i helped... link me if u need nemore help

x=pencils
y=pen
==============
4x+5y=2.00
3x+4y=1.48
solve for x and y

S+B=199.00
S=B+51
==============
solve for S and B

For Problem #1
I get
x= 0.20
y = 0.24

for problem #2
I get
s=125
b=74

dentify the information that is needed to solve the problem.


A store has a special offer on a pack of 12 pencils, 4 pens, and 8 colored markers. The special price is $12.50 for the pack. What fraction of the tools are pencils?

5 pens and pencils cost $55.00 and 3 pens and 5 pencils cost $41.00. Find the cost for 4 pens and 3 pencils

To solve the equations for the first problem, you need to use a method called substitution or elimination. Let's use the substitution method:

The given equations are:
4P + 5N = 2.00
3P + 4N = 1.58

First, rearrange the second equation to solve for one variable in terms of the other. Let's solve for P:
3P = 1.58 - 4N
P = (1.58 - 4N) / 3

Substitute this value of P into the first equation:
4((1.58 - 4N) / 3) + 5N = 2.00

Now, simplify and solve for N:
(6.32 - 16N) / 3 + 5N = 2.00
6.32 - 16N + 15N = 2.00 * 3
6.32 - N = 6.00
-N = 6.00 - 6.32
-N = -0.32
N = 0.32

Substitute the value of N back into one of the original equations to solve for P:
3P + 4 * 0.32 = 1.58
3P + 1.28 = 1.58
3P = 1.58 - 1.28
3P = 0.30
P = 0.10

Therefore, the cost of a pencil (P) is $0.10 and the cost of a pen (N) is $0.32.

To solve the equations for the second problem, we can use a similar approach:

Given equations:
S + B = 199.00
S = B - 51.00

Substitute the value of S from the second equation into the first equation:
(B - 51) + B = 199
2B - 51 = 199
2B = 199 + 51
2B = 250
B = 250 / 2
B = 125

Substitute the value of B back into the second equation to solve for S:
S = 125 - 51
S = 74

Therefore, the cost of the skateboard (S) is $74.00 and the cost of the bicycle (B) is $125.00.