eddy2017
Elite Member
- Joined
- Oct 27, 2017
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Hi, another student posted this. It is an interesting problem.
An investor buys a total of 275 shares of two stocks: Company A and Company B. Company A is priced at $24 per share. Company B is priced at $17 per share. The investor spends a total of $5,459. 275 being the number of shares bought you need to find how many of each stock (Stock A and B) is purchased to reach the total of $5459.
Revisiting older problems here i have done with your help. i have tried to follow the method. let me see if I have done the right way
I have asked myself these questions. ( they're good to ask in a word problem where linear equations are involved
Let x be the number of shares bought from company A
and y the number of shares bought from company B.
1) What's the equation corresponding to the information that a total of 275 shares was bought?
2) What's the equation corresponding to the information that a total of $ 5459 was spent, given that a share from A costs $ 24 and one share of B is priced at $ 17?
3) What are your first steps to solve this system of equations?
let's explain what the variables stand for.
x= number of shares from A
y= number of shares from B
now, let's procced to formulate one equation oof of this statement
275 being the number of shares bought you need to find how many of each stock (Stock A and B) is purchased to reach the total of $5459.
[math]x + y= 275[/math]
and then let's proceed to formulate the other equation off of this question i asked me at the beginning
what's the equation corresponding to the information that a total of $ 5459 was spent, given that a share from A costs $ 24 and one share of B is priced at $ 17?
[math]24x + 17x * (275-x) =5459[/math] remember that y= 275-x so you're just replacing y for its value.
now that we have the two equations set up we solve for one first
let's solve for x first
[math]24x+17(275−x)=5459[/math]
Simplify both sides of the equation by distributing
[math]24x+(17)(275)+(17)(−x)=5459[/math]
[math]24x+4675+−17x=5459[/math]
Combining like terms
[math](24x+−17x)+(4675)=5459[/math]
[math]7x+4675=5459[/math]
Subtractin’ 4675 from both sides.
[math]7x+4675−4675=5459−4675[/math]
[math]7x=784[/math]
Dividin’ both sides by 7.
[math]x=112[/math]
Company A purchases 112 sotcks
now, let’s solve for y which is the easiest part having the value of x
[math]y= 275 –x[/math]
[math]y =275- 112[/math]
[math]y=163[/math]Company B purchases 163 stocks
checking
[math]122 + 163=[/math]=275
An investor buys a total of 275 shares of two stocks: Company A and Company B. Company A is priced at $24 per share. Company B is priced at $17 per share. The investor spends a total of $5,459. 275 being the number of shares bought you need to find how many of each stock (Stock A and B) is purchased to reach the total of $5459.
Revisiting older problems here i have done with your help. i have tried to follow the method. let me see if I have done the right way
I have asked myself these questions. ( they're good to ask in a word problem where linear equations are involved
Let x be the number of shares bought from company A
and y the number of shares bought from company B.
1) What's the equation corresponding to the information that a total of 275 shares was bought?
2) What's the equation corresponding to the information that a total of $ 5459 was spent, given that a share from A costs $ 24 and one share of B is priced at $ 17?
3) What are your first steps to solve this system of equations?
let's explain what the variables stand for.
x= number of shares from A
y= number of shares from B
now, let's procced to formulate one equation oof of this statement
275 being the number of shares bought you need to find how many of each stock (Stock A and B) is purchased to reach the total of $5459.
[math]x + y= 275[/math]
and then let's proceed to formulate the other equation off of this question i asked me at the beginning
what's the equation corresponding to the information that a total of $ 5459 was spent, given that a share from A costs $ 24 and one share of B is priced at $ 17?
[math]24x + 17x * (275-x) =5459[/math] remember that y= 275-x so you're just replacing y for its value.
now that we have the two equations set up we solve for one first
let's solve for x first
[math]24x+17(275−x)=5459[/math]
Simplify both sides of the equation by distributing
[math]24x+(17)(275)+(17)(−x)=5459[/math]
[math]24x+4675+−17x=5459[/math]
Combining like terms
[math](24x+−17x)+(4675)=5459[/math]
[math]7x+4675=5459[/math]
Subtractin’ 4675 from both sides.
[math]7x+4675−4675=5459−4675[/math]
[math]7x=784[/math]
Dividin’ both sides by 7.
[math]x=112[/math]
Company A purchases 112 sotcks
now, let’s solve for y which is the easiest part having the value of x
[math]y= 275 –x[/math]
[math]y =275- 112[/math]
[math]y=163[/math]Company B purchases 163 stocks
checking
[math]122 + 163=[/math]=275