John took all his money out of his savings account. He spent $50 on a radio and 3/5 of what remained on presents. Half of what was left he put back in his checking account, and the remaining $35 he donated to charity. How much money did John originally have in his savings account?
Original amount=X Dollars.
Bought 50 dollar radio.
Bal.=X-50
(X-50)-3/5*(X-50)=2/5*(X-50) Bal.
1/2*2/5*(X-50)=1/5*(X-50) Bal.
1/5*(X-50)=35. Solve for X:
X=225=Original Amt.
Let's calculate step-by-step.
Let's assume that the amount of money John originally had in his savings account is represented by "x" dollars.
Step 1: John spent $50 on a radio, which means the amount of money remaining in his savings account is now x - $50.
Step 2: John spent 3/5 of what remained on presents. This means he spent 3/5 * (x - $50) on presents. So the amount of money remaining in his account after buying presents is (x - $50) - (3/5 * (x - $50)).
Step 3: Half of what was left, which is (x - $50) - (3/5 * (x - $50)), was put back in his checking account. So the amount of money remaining after putting half back in his checking account is 1/2 * [(x - $50) - (3/5 * (x - $50))].
Step 4: The remaining $35 was donated to charity, which means the amount of money remaining in his account after the donation is 1/2 * [(x - $50) - (3/5 * (x - $50))] - $35.
Now, we can set up an equation to solve for x:
1/2 * [(x - $50) - (3/5 * (x - $50))] - $35 = 0
Simplifying the equation:
1/2 * [(5/5 * (x - $50)) - (3/5 * (x - $50))] - $35 = 0
1/2 * [(2/5 * (x - $50))] - $35 = 0
(1/2 * 2/5) * (x - $50) - $35 = 0
1/5 * (x - $50) - $35 = 0
1/5 * x - 1/5 * $50 - $35 = 0
1/5 * x - $10 - $35 = 0
1/5 * x - $45 = 0
1/5 * x = $45
x = $45 * 5
x = $225
Therefore, John originally had $225 in his savings account.
To find out how much money John originally had in his savings account, let's break down the information provided step by step.
1. John spent $50 on a radio.
2. After buying the radio, John had (100% - 50% = 50%) of his original savings remaining.
3. John spent 3/5 of what remained on presents.
To find out how much John spent on presents, we need to calculate (3/5) * 50% of his original savings.
(3/5) * 50% = 3/10 = 0.3
So, John spent 0.3 * his original savings on presents.
4. After spending on presents, John had (100% - 0.3) * 50% = 70% * 50% = 0.7 * 0.5 = 35% of his original savings remaining.
5. John put half of what was left in his checking account.
To calculate this amount, we need to calculate 35% * 50% of his original savings.
35% * 50% = 0.35 * 0.5 = 0.175
So, John put 0.175 * his original savings into his checking account.
6. The remaining $35 that John donated to charity represents 35% of his original savings.
Therefore, 35% of his original savings equals $35.
To find his original savings, we can calculate: Original Savings = ($35 * 100%) / (35%).
Simplifying this equation gives us: Original Savings = $35 / 0.35.
7. Therefore, John originally had $100 in his savings account (since $35 / 0.35 = $100).
So, John originally had $100 in his savings account.