3-) Martha O'Brien made a deposit to her checking account at an ATM and received $75 in cash. The checks deposited totaled $50 less than twice the currency amount,
and the total deposit was $25 more than the check amount. Determine the amounts
Martha deposited in checks and in currency as well as the total deposit.

The amount Martha deposited in checks is $150

The amount Martha deposited in cash is $100

The total deposit is $175

Step-by-step explanation:

Since Total deposit (T) = currency (C) + coins + check (Ck) - cash received (Csh)

T = C + Ck - Csh.  (1)

Given that cash received (Csh) = $75,coins = 0 and the checks deposited totaled $50 less than twice the currency amount. So,

Ck = 2C - $50   (2)

Also, total deposit was $25 more than the check amount. So,

T = Ck + $25  (3)

Substituting equation (2) into (1), we have

T = C + Ck - Csh

T = C + 2C - $50 - Csh

T = 3C - $50 - $75

T = 3C - $125   (4)

Substituting equation (2) into (3), we have

T = Ck + $25

T = 2C - $50  + $25

T = 2C - $25  (5)

Equating equations (4) and (5), we have

3C - $125 = 2C - $25

Collecting like terms, we have

3C - 2C = $125 - $25

C = $100  

Substituting C into (2), we have

Ck = 2C - $50  

Ck = 2($100) - $50  

Ck = $200 - $50

Ck = $150

We now compute T

T = C + Ck - Csh.

T = $100 + $150 - $75.

T = $250 - $75

T = $175

So, the amount Martha deposited in checks is $150

The amount Martha deposited in cash is $100

The total deposit is $175

answer: e 9, 5.75

step-by-step explanation:

step 1

find the variation ab in the x coordinate

delta x=(x2-x1)=10-> 8 units

find the variation ab  in the y coordinate 

delta y=(y2-y1)=6-> 2 units

step 2

find the coordinates point c

  x coordinate 

cx=ax+delta x*2/> cx=2+8*(2/> cx=3

  y coordinate 

cy=ay+delta y*2/> cy=4+2*(2/> cy=4.25

the coordinates of point c are (3,4.25)

step 3

find the coordinates point d

  x  coordinate 

dx=ax+delta x*4/> dx=2+8*(4/> dx=4

  y  coordinate 

dy=ay+delta y*4/> dy=4+2*(4/> dy=4.5

the coordinates of point d are (4, 4.5)

step 4

find the coordinates point e

  x  coordinate 

ex=ax+delta x*4/> ex=2+8*(6/> ex=5

  y  coordinate 

ey=ay+delta y*4/> ey=4+2*(6/> ey=4.75

the coordinates of point e are (5, 4.75)

step 5

find the coordinates point f

  x  coordinate 

fx=ax+delta x*4/> fx=2+8*(8/> fx=6

  y  coordinate 

fy=ay+delta y*4/> fy=4+2*(8/> fy=5

the coordinates of point f are (6,5)

step 6

find the coordinates point g

  x  coordinate 

gx=ax+delta x*4/> gx=2+8*(10/> gx=7

  y  coordinate 

gy=ay+delta y*4/> gy=4+2*(10/> gy=5.25

the coordinates of point g are (7,5.25)

step 7

find the coordinates point h

  x  coordinate 

hx=ax+delta x*4/> hx=2+8*(12/> hx=8

  y  coordinate 

hy=ay+delta y*4/> hy=4+2*(12/> hy=5.5

the coordinates of point h are (8,5.5)

step 8

find the coordinates point i

  x  coordinate 

ix=ax+delta x*4/> ix=2+8*(14/> ix=9

  y  coordinate 

iy=ay+delta y*4/> iy=4+2*(14/> iy=5.75

the coordinates of point i are (9,5.75)

- r3ktforgood ☕