can somone help me with this one , what equations do i have to use or what do i have to to inorder to see if this is possible
Lori Morgan has $16,000 invested in Disney and Intel Stock. The Disney stock currently sells for $30 a share and Intel stock for $70 a share. Her stockbroker points out that if Disney stock goes up 50% and Intel stock goes up to $35 a share, her stock will be worth $25,500. IS this possible?
30D + 70I=16000 where D, I are number of shares.
(30*1.50)D+ (70+35)I=25500
I read the problem as (Intel goes up by 35 dollars. I am not certain what you meant...if it was 70 dollars a share, it cannot go up to 35 dollars a share.
So you solve these equations to see if there is a solution.
30D + 70I=16000
45D+ 105I=25500
I can see there is no solution. Disney went up most, so say the number of I shares was zero, increasing Disney by 50 percent (16000+ 8000)=24000.
To determine if it is possible for Lori's stock to be worth $25,500, you need to use the given information to set up the equations and solve for the unknown variables.
Let D be the number of Disney shares and I be the number of Intel shares.
From the given information, you know that Lori has $16,000 invested, so you can set up the equation:
30D + 70I = 16,000
The stockbroker points out that if Disney stock goes up 50% and Intel stock goes up to $35 a share, then the value of her stocks will be $25,500. This information can be used to set up another equation:
(30 * 1.5)D + (70 + 35)I = 25,500
Now, you have a system of equations:
30D + 70I = 16,000
45D + 105I = 25,500
To find if there is a solution, you can solve these equations using various techniques such as substitution, elimination, or matrix methods. For simplicity, let's use the elimination method:
Multiply the first equation by 3 to make the coefficient of D in both equations the same:
90D + 210I = 48,000
Subtract the two equations:
(90D + 210I) - (45D + 105I) = 48,000 - 25,500
45D + 105I - 45D - 105I = 22,500
0 = 22,500
This is a contradiction since 0 cannot equal 22,500. Therefore, there is no solution to this system of equations.
Based on the calculations, it is not possible for Lori's stock to be worth $25,500 if Disney stock goes up 50% and Intel stock goes up to $35 a share.