please help -
lisa had a collection of stamps from australia, france and japan. she had 124 stamps from australia. 30% of the stamps were from France. she had 12 fewer stamps from japan than australia.
a) what was the total number of stamps in Lisa's collection?
b) Lisa's aunt gave hers some stamps from France. Her total collection increased by 25%. what % of her collection was from france after that?
a. X stamps, Total.
124 stamps, Australia
0.3x stamps, France
0.3x-12 stamps, Japan
X = 124 + 0.3x + 0.3x-12
0.4x = 112
X = 280
b. 280 + n = 1.25*280 = 350
n = 70 Stamps from Lisa's aunt.
(0.3x+n)/350 = (84+70)/350 = 0.44 = 44%
from France.
I don understand
a) To find the total number of stamps in Lisa's collection, we need to add the number of stamps from each country.
Number of stamps from Australia = 124
Number of stamps from France = 30% of the total number of stamps
Number of stamps from Japan = Number of stamps from Australia - 12
To find the total number of stamps, we can add these numbers together:
Total number of stamps = Number of stamps from Australia + Number of stamps from France + Number of stamps from Japan
Total number of stamps = 124 + (30% of total number of stamps) + (Number of stamps from Australia - 12)
Since we don't know the total number of stamps yet, we can represent it as 'S.'
Total number of stamps = 124 + (30% of S) + (124 - 12)
Simplifying the equation:
Total number of stamps = 112 + 0.3S
Now, we can solve for S:
S - 0.3S = 112
0.7S = 112
S = 112 / 0.7
S ≈ 160
Therefore, the total number of stamps in Lisa's collection is approximately 160.
b) After Lisa's aunt gave her some stamps from France, her collection increased by 25%. To find the percentage of her collection that was from France after that, we need to calculate the number of stamps from France and divide it by the new total number of stamps in her collection.
Since 30% of Lisa's previous total number of stamps were from France, we can calculate the new number of stamps from France:
New number of stamps from France = 30% of 160
New number of stamps from France = 0.3 * 160
New number of stamps from France = 48
Now, the new total number of stamps in Lisa's collection is 125% of the previous total:
New total number of stamps = 125% of 160
New total number of stamps = 1.25 * 160
New total number of stamps = 200
To find the percentage of her collection that was from France after the increase, we can divide the new number of stamps from France by the new total number of stamps:
Percentage of collection from France = (New number of stamps from France / New total number of stamps) * 100
Percentage of collection from France = (48 / 200) * 100
Percentage of collection from France ≈ 24
Therefore, after Lisa's aunt gave her some stamps from France, approximately 24% of her collection was from France.
To find the answers to these questions, let's break down the information given step by step:
a) To find the total number of stamps in Lisa's collection, we need to add the number of stamps from each country.
From the information, we know that Lisa had 124 stamps from Australia.
We are also given that 30% of the stamps in her collection were from France. To find the number of stamps from France, we can calculate 30% of the total number of stamps in her collection.
Let's suppose the total number of stamps in her collection is "x." Therefore, 30% of x is the number of stamps from France. Mathematically, this can be represented as 0.3x.
We then know that Lisa had 12 fewer stamps from Japan than from Australia. This means the number of stamps from Japan is 124 - 12, which simplifies to 112.
Now, we can add all three quantities to find the total number of stamps:
Total = Stamps from Australia + Stamps from France + Stamps from Japan
Total = 124 + 0.3x + 112
Therefore, the total number of stamps in Lisa's collection is 236 + 0.3x.
b) Lisa's aunt gives her some additional stamps from France, increasing her total collection by 25%. We need to find the new percentage of stamps from France out of the updated total.
Let's use the previous total, which we found to be 236 + 0.3x.
To increase the total collection by 25%, we need to multiply the total by 1.25 (since 1 + 0.25 = 1.25).
So, the new total is (236 + 0.3x) * 1.25.
To find the new percentage of stamps from France, we divide the number of stamps from France (0.3x) by the new total and convert it to a percentage.
Percentage of stamps from France = (0.3x / new total) * 100.
By substituting the value of the new total, we can calculate the exact percentage.
Remember to always simplify or calculate any expressions given in a problem before arriving at the final answer.