Aisha owns an apparel store. She bought some shirts and jeans from a wholesaler for $3,900. Each shirt cost $12 and each pair of
jeans cost $28. If she sold the shirts at 70% profit and jeans at 125% profit, her total profit was $3,885. How many shirts and jeans did she buy from the wholesalers? 101 shirts and 96 jeans
2 answers:
For this case we can define the following variables:
x: shirt
y: jeans
We write the following system of equations:
12x + 28y = 3900
8.4x + 35y = 3885
We solve the system of equations:
x = 150
y = 75
Note: see attached image for the solution of the system:
Answer:
she bougth from the wholesalers
150 shirts
75 jeans
x: shirt
y: jeans
We write the following system of equations:
12x + 28y = 3900
8.4x + 35y = 3885
We solve the system of equations:
x = 150
y = 75
Note: see attached image for the solution of the system:
Answer:
she bougth from the wholesalers
150 shirts
75 jeans
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Answer:
1. y = 2(3)ˣ; 2. y = 10(4)^x; 4. Amber = 192 and 3 145 728;
Ben has 54 and 11 098; Carter = 80 and 10 249 shares;
5. Shifted up 45 shares; 6. Amber's;
7. Fewer friends. more shares.
Step-by-step explanation:
The general equation for an exponential function is
y = a(b)ˣ
1. Ben's function
The initial value a = 2.
6 = 2(b)¹ = 2b
Ben's function is
y = 2(3)^x
2. Carter's function
Carter shared his post with 10 friends on Day 0, so a= 10.
Each friend shared with 2 people each day, so b = 2.
Therefore, Carter's function is
y=10(2)ˣ
3. Graphs
The figure below shows the graphs for each function.
4. Predictions
(a) Amber
(i) Day 3
y = 3(4)³ = 3 × 64 = 192
(ii) Day 10
y = 3(4)¹⁰ = 3 × 1 048 576 = 3 145 728
(b) Ben
(i) Day 3
y = 2(3)³ = 2 × 27 = 54
(ii) Day 10
y = 2(3)¹⁰ = 2 × 29 049 = 118 098
(c) Carter
(i) Day 3
y = 10(2)³ = 10 × 8 = 80
(ii) Day 10
y =10(2)¹⁰ = 10 × 1024 = 10 240
5. Sharing with assisted living facility
y = 3(4)ˣ + 45
The new graph will be shifted up by 45 units.
6. Fastest post
Amber's post travels the fastest.
After only two days, she already has more posts than anyone else.
By Day 10, she has more than 25 times the shares of her closest competitor.
7. Preference
It's not the number of friends you have, but the number of shares they make, that is the important factor.
Carter started with 10 friends, but they made only two shares.
Amber started with only three friends, but they made four shares. By Day 3, she had 192 shares compared to 82 for Carter and only 54 for Ben
If I had to choose, I would prefer a post with fewer friends initially but more shares, like Amber.
