Fred is closing a bank account t and wants to distribute the money among his grandchildren by giving each of them $20. To do this Fred needs an additional $62 . Instead he gave each grandchild $17 and had $7 left over. How many grandchildren does Fred have? How much money did he have in the bank account?

let the number of grandchildren he has be n

so total money = 17n + 7

20n = 17n+7 + 62
3n = 69
n = 23

total money = 17(23)+7 = $ 398
And he has 23 grandkids

check:
if he wanted to give each $20,
he would need $ 460,
But he has only 398, which is $ 62 short of what he needs.

He has 23 grandchildren, WOW

Let's break down the information given step-by-step to find the answers:

1. Let's assume the number of grandchildren is "x".
2. Fred wanted to give each grandchild $20, so the total amount he initially planned to distribute to all the grandchildren was 20x dollars.
3. However, Fred needed an additional $62 to distribute the money as planned. This means that the total amount of money he had in the bank account was 20x + 62 dollars.
4. Instead, Fred gave each grandchild $17, which means he distributed a total of 17x dollars.
5. Fred had $7 left over after distributing the money. Therefore, the remaining amount in his bank account is 7 dollars.
6. We can now set up an equation to solve for "x":

(amount initially planned to distribute) - (amount actually distributed) - (remaining amount) = 0
(20x + 62) - (17x) - 7 = 0

7. Simplifying the equation:

20x + 62 - 17x - 7 = 0
3x + 55 = 0

8. Solving for "x":

3x = -55
x = -55/3
x ≈ -18.33

9. Since "x" represents the number of grandchildren, it cannot be a negative or decimal value. Hence, we can conclude that there may be some error in the given information.

Based on the given information, it is not possible to determine the exact number of grandchildren Fred has or the exact amount of money he had in the bank account.

To solve this problem, we can use a system of equations. Let's define the variables:

Let's say the number of grandchildren is represented by 'x'.
The amount of money in the bank account can be represented by 'b'.

According to the problem, we have two pieces of information:

1. Fred wants to distribute the money among his grandchildren by giving each of them $20, which requires an additional $62.

We can express this information in the equation:
20x + 62 = b

2. Instead, Fred gives each grandchild $17 and has $7 left over.

We can express this information in a second equation:
17x + 7 = b

By setting these two equations equal to each other, we can solve for 'x', the number of grandchildren.

20x + 62 = 17x + 7

Simplifying the equation, we get:
3x = 55

Dividing both sides of the equation by 3, we find that:
x = 55/3

Since the number of grandchildren must be a whole number, we round up to the nearest whole number, which is 19.

Therefore, Fred has 19 grandchildren.

To find the amount of money Fred had in the bank account, we substitute the value of 'x' back into either of the original equations.

Using the first equation:
20x + 62 = b
20(19) + 62 = b
380 + 62 = b
442 = b

Therefore, Fred had $442 in the bank account.