Ivan spent 1/4 of his money on a watch. He spent 2/5
of the remainder on 3
Identical shirts and saved the rest.
(a)
What fraction of Ivan's money was pent on the 3 shirts?
(b)
The watch cost $120 more than one shirt. How much money dld Ivan
save?
(a) 2/5 * 3/4 = 3/10 of total
so a shirt is 1/10 of total
so
1/4 on watch
3/10 on shirts
watch = 1/4 total = 120 + 1/10 total
(5/20 - 2/20) total = 120
3 * total = 2400
total = 600
watch = 180
shirts =180
remainder = 240 saved
3 * total = 2400
total = 800
...
(a) To find the fraction of Ivan's money spent on the 3 shirts, we first need to find the remaining fraction of his money after buying the watch.
Let's say Ivan had x money initially.
He spent 1/4 of his money on a watch, which is equal to (1/4)x = x/4.
The remainder of his money after buying the watch is (1 - 1/4)x = (3/4)x.
Next, Ivan spent 2/5 of the remainder on the 3 identical shirts.
The amount of money spent on shirts is (2/5) * (3/4)x = (6/20)x = (3/10)x.
Therefore, the fraction of Ivan's money spent on the 3 shirts is (3/10).
(b) We are given that the watch cost $120 more than one shirt.
Let's say the cost of a single shirt is s.
Therefore, the cost of the watch is s + $120.
We know that Ivan spent 1/4 of his money on the watch and 2/5 of the remainder on shirts, and the rest of his money was saved.
So, we can write the equation:
(3/4)x - (2/5) * (3/4)x - (s + $120) = savings
Simplifying this equation, we get:
(3/4)x - (6/20)x - (s + $120) = savings
(15/20)x - (6/20)x - (s + $120) = savings
(9/20)x - (s + $120) = savings
Since the equation includes two unknowns (x and s), we cannot find the exact amount of savings without any additional information.
To find the fraction of Ivan's money spent on the 3 shirts, we first need to determine the amount of money he had after buying the watch.
(a) Let's say Ivan had x amount of money initially.
Ivan spent 1/4 of his money on the watch, so the remaining fraction of money he had is 1 - 1/4 = 3/4.
He then spent 2/5 of the remaining money on 3 identical shirts. So the fraction of money spent on the shirts is (2/5) * (3/4) = 6/20.
Simplifying the fraction, we get 6/20 = 3/10.
Therefore, Ivan spent 3/10 of his money on the 3 shirts.
(b) The watch cost $120 more than one shirt. Let's say the cost of one shirt is y dollars.
The watch cost y + $120.
Ivan spent 1/4 of his money on the watch, so he spent 1/4 of x dollars.
Hence, (1/4) * x = y + $120.
To find out how much money Ivan saved, we need to determine the amount of money left after buying the watch and the shirts.
The remaining fraction of money after buying the watch is 3/4.
Ivan spent 2/5 of the remaining money on 3 identical shirts, which is (2/5) * (3/4) * x.
Therefore, the amount of money Ivan saved is (3/4) * x - (2/5) * (3/4) * x.
Simplifying further, we get (3/4) * x - (6/20) * (3/4) * x.
(3/4) * x - (6/20) * (3/4) * x = (3/4) * x - (18/80) * x.
Simplifying the terms, we get (3/4) * x - (9/40) * x.
To calculate the exact amount of money saved, we need the value of x.
Therefore, to find the exact amount of money saved, we need to know the initial amount of money Ivan had (x).