Mathematics, 09.07.2019 02:40 noahtheking67

Keith has p pennies, n nickels, and d dimes in his pocket. the total number of coins is 9. the expression 0.01p+0.05n+0.10d represents the value of the coins, which is equal to $0.44. he has one more dime than nickels. how many pennies does keith have? keith has pennies.

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Answer from: madiforkner

Keith has 4 pennies, 3 dimes and 2 nickels.

Step-by-step explanation:

Let the pennies be = p

Let the nickels be = n

Let the dimes be = d

Total coins Keith has = 9

So, 1st equation form :

p+n+d=9 ....(1)

Keith has one more dime than nickels, means d=n+1 .....(2)

Total value of these coins is $0.44

So, third equation forms:

0.01p+0.05n+0.10d=0.44 .....(3)

Substituting (2) in (1)

p+n+n+1=9

p+2n=8 .....(4)

Similarly substitution (2) in (3)

0.01p+0.05n+0.10(n+1)=0.44

0.01p+0.05n+0.10n+0.10=0.44

0.01p+0.15n=0.34 ....(5)

Now multiplying (4) by 0.01 and subtracting by (5)

0.01p+0.02n=0.08 subtracting this from (5) we get

0.13n=0.26

So, we get n = 2

p+2n=8

p+2(2)=8

p+4=8

p = 4

p+n+d=9

4+2+d=9

6+d=9

d = 3

-------------------------------------------------------------------------------------

Therefore, Keith has 4 pennies, 3 dimes and 2 nickels.

Answer from: Quest

Abit confused about what you mean, but i think you might be referring to slope intercept form: y = mx + bin that case b, or the y intercept is already given.(0,-1)find the slope by using the formulay2 - y1/x2 - x1the final slope will be 4/2, equivalent to 2.now your equation should look like thisy = 4/2x -1sorry if this didn’t you out!

Answer from: Quest

$a_1 = 1$ , and

$a_{n+1} = a_n + (n + 1)$ for $n \ge 1$

step-by-step explanation:

we can analyze the pattern at which the terms increase. let us denote $a_1 = 1$ , $a_2 = 3$ , $a_3 = 6$ , so that we can call

1 the 1st term, 3 the 2nd term, 6 the 3rd term,etc.

note the following:

from the 1st term (1) to the 2nd term (3), we go up by 2,from the 2nd term (3) to the 3rd term (6), we go up by 3from the 3rd term (6) to the 4th term (10), we go up by 4, andfrom the 4th term (10) to the 5th term (15), we go up by 5.

the pattern: to get the next term value, we just add the next term number (e.g. 1st, 2nd, to the previous term value (term values are the given numbers in the question, 1, 3, 6, 10, 15,

from $a_1 = 1$ , to get to $a_2 = 3$ , we add $2(=1+1)$

from $a_2 = 3$ , to get to $a_3 = 6$ , we add $3 (=2+1)$

etc.

we need to form a recursive formula, a formula that has the next term as a function of the previous term. so a possible recursive formula can be

$a_1 = 1$ , and $a_{n+1} = a_n +(n + 1)$ for $n \ge 1$

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Keith has p pennies, n nickels, and d dimes in his pocket. the total number of coins is 9. the expre...