Alex spent 1/3 of his pocket money on a toy airplane and 2/3 of the remainder on a toy robot. He had $20 left. How much did
he spend altogether?
He spent $70 in total! He spent ⅓ of his money on a toy plane remainder ³/³ -
⅓ = ⅔. Spent on toy robot = 2/3 * 2/3 = 4/9
Total spent = 1/3 + 4/9 = 3/9 + 4/9 = 7/9
Left = 9/9 - 7/9 = 2/9
Then the final step,
2/9 to $20
1/9 to 20/2 = $10
7/9 to 10*9 = $70
x is total he started with
he spent 1/3 x and 2/3*2/3 = 4/9 x
3/9 + 4/9 = 7/9 x spent
left is 2/9 x = $20
so x = 180/2 = $ 90 to start
left with $20 so spent $70
Nah is hard I can under With unit block
Well, it seems like Alex is taking the concept of "spending like there's no tomorrow" to a whole new level! But let's break it down. If he had $20 left after spending 2/3 of the remaining money on a toy robot, we can assume that this remaining money is 1/3 of his original pocket money. Therefore, his original pocket money would've been 3 times the remaining money, which is $20 x 3 = $60.
To find out how much he spent altogether, we add up what he spent on the toy airplane and the toy robot. He spent 1/3 of his pocket money on the toy airplane, which is $60 x 1/3 = $20. And then he spent 2/3 of the remaining money on the toy robot, which is $20 x 2/3 = $13.33 (approximately).
So, if we add up these amounts, Alex spent a grand total of $20 + $13.33 = $33.33 (approximately). I hope all those toys were worth it!
To find out how much Alex spent altogether, we need to add up the amounts he spent on the toy airplane and the toy robot.
Let's calculate step by step:
1. Let's assume Alex's total pocket money is X dollars.
2. Alex spent 1/3 of his pocket money on a toy airplane. The amount he spent on the toy airplane is (1/3) * X dollars.
3. The remainder after buying the toy airplane is given by X - (1/3) * X = (2/3) * X.
4. Alex spent 2/3 of the remainder on a toy robot. The amount he spent on the toy robot is (2/3) * [(2/3) * X] dollars.
5. The total amount he spent is the sum of the amounts he spent on the toy airplane and the toy robot. So, we add these two amounts together:
Total amount spent = (1/3) * X + (2/3) * [(2/3) * X]
= (1/3) * X + (4/9) * X
= (3/9) * X + (4/9) * X
= (7/9) * X
Given that Alex had $20 left, we can set up an equation:
Total amount spent + $20 = X
Now, we can solve for X:
(7/9) * X + $20 = X
Subtracting (7/9) * X from both sides yields:
$20 = (2/9) * X
Dividing both sides by (2/9) gives:
X = ($20 * 9) / 2
X = $90 / 2
X = $45
So, Alex's total pocket money is $45.
Finally, we can substitute the value of X into the equation for the total amount spent:
Total amount spent = (7/9) * $45
= $35
Therefore, Alex spent a total of $35 altogether.