Evan's uncle gave him money for his birthday. He puts half of the money in his savings account, spends \(\frac{1}{5}\) of the money on bubble gum to share with his friends, and buys comics with the rest. What portion of the money will he spend on comic books?
Evan uses some of his comic book money to buy a magazine for $4. If Evan's uncle gave him $30, what fraction of the money did he spend on the magazine?
Answer (3)
Let
x-------> amount that Evans uncle gave for the birthday
**Part a) **What portion of money will he spend on comic books?
we know that
Evan puts half of the money in his savings account
so
x − 2 x = 2 x
the rest is equal to 2 x
Evan spend 5 1 of the money on bubble gum to share with his friends
2 x − 5 x = 10 ( 5 x − 2 x ) = 10 3 x
the rest is equal to 10 3 x
Evan buy comics with the rest
the rest is equal to 10 3 x
therefore
the answer Part a) is
The portion of money that Evan will spend on comic books is 10 3
Part b) Evans uses some of his comic book money to buy a magazine for $4. Evans uncle gave him $30, what fraction of the money did he spend on he magazine
The portion of money that Evan will spend on comic books is 10 3 x
x = 30
So
10 3 ∗ 30 = 9 $
by using proportion
1 9 = x 4 9 ∗ x = 4 x = 9 4
therefore
If the question refers to the fraction with respect to the money used for the comics
then
**the answer Part b1) is **
9 4
If the question refers to the fraction with respect to the total money
then
by using proportion
1 30 = x 4 30 ∗ x = 4 x = 30 4
30 4 = 15 2
**the answer Part b2) is **
15 2
1/2 of the money put in savings and 1/5 of the money spent on bubble gum gives us:
1/2 + 1/5 = 5/10 + 2/10 = 7/10 of the money.
So he spent 3/10 of the moeny on comic books (because 1 - 7/10 = 3/10).
Now 3/10 of $30 is:
30 * 3/10 = 3 * 3/1 = 9
So Evan had $9 for comic books and he spent 4/9 of of his comic books money for the magazine.
Evan will spend 10 3 of the money on comic books and 9 4 of his comic book money on the magazine. He initially received $30, saved $15, spent $6 on bubble gum, and had $9 left for comics. When he bought a magazine for $4, it amounted to 9 4 of his comic book funds.
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