Mathematics, 06.10.2019 11:00 jadalysrodriguez

Me with 2 and 3 and use the elimination process!

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Answer from: paige1616

2. Judy =$5

Ben= $4

Step-by-step explanation:

2. Let Judy = x and Ben = y

8x + 10y = 80

9x + 5y = 65

Solve these simultaneous equations.

8 x + 10 y = 80

18 x + 10 y = 130

Take the second equation away from the first equation

− 10 x = − 50

x = 5

This means that Judy gets paid $5 an hour.

Therefore, Ben gets paid $4 an hour.

3. 24 quarters and 16 dimes

Step-by-step explanation:

3. Let the number of dimes = x and the number of quarters = y

Value Value

Type Number of of

of of EACH ALL

coin coins coin coins

dimes x $0.10 $0.10x

quarters y $0.25 $0.25y

TOTALS 40 $7.60

x + y = 40

0.10x + 0.25y = 7.60

Get rid of decimals by multiplying every term by 100:

10x + 25y = 760

So we have the system of equations:

x + y = 40

10x + 25y = 760

We solve by substitution. Solve the first equation for y:

x + y = 40

y = 40 - x

Substitute (40 - x) for y in 10x + 25y = 760

10x + 25(40 - x) = 760

10x + 1000 - 25x = 760

-15x + 1000 = 760

-15x = -240

x = 16 = the number of dimes.

Substitute in y = 40 - x

y = 40 - (16)

y = 24 quarters.

$1.60 + $6.00 = $7.60

I hope that helped, sorry for taking so long :-)

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 $n \ge 1$

Answer from: Quest

Ihave, but this question is gonna probably get deleted.

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