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

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step-by-step explanation: