Thread: Please Need Help Fast World Problems

I am suppose to list variables and give equations. I have six word problems in my homework that I can not seem to figure out I know that of at least 3 that have to use the supply and demand model and another one has to do with mixtures plus motion. I would truly appreciate the help Check them out below:

1. A company budgets $30,000 for advertisement costs promoting a new product. Television ads cost $500 each and radio ads cost $100 each. If the company wants to buy a total of 220 ads, how many of each kind of ads should the company buy?

2. A charity sells tickets for a fundraising dinner. Each adult's ticket costs $10 and each child's ticket costs $5. A total of $1050 was raised by selling 130 tickets. How many of each kind of ticket was sold?

3. A chemist needs 110 milliters of a 31% solution but has only 10% and 43% solutions available. How many milliters of each should be mixed to get the desired solution?

4. The weekly demand model for a new toy is given by D=-5p+80. The weekly supply model for the same toy is 5=3p+40. For these models, p is the price of the toy and N is the number of toys sold or supplied each week to the toy store. Find the price at which supply and demand are equal.

5. A college student earned $8200 during summer vacation working as a waiter in a popular restaurant. The student invested part of the money at 8% and the rest at 7%. If the student received a total of $613 in interest at the end of the year. How much was invested at 8%?

6. A twin-engined aircraft can fly 816 mi. from city A to city B in 3 hrs. with the wind and make the return trip in 8 hrs. against the wind. What is the speed of the wind?

I have been trying all night to figure out these word problems Please help

Originally Posted by MathIlliterate

I am suppose to list variables and give equations. I have six word problems in my homework that I can not seem to figure out I know that of at least 3 that have to use the supply and demand model and another one has to do with mixtures plus motion. I would truly appreciate the help Check them out below:

1. A company budgets $30,000 for advertisement costs promoting a new product. Television ads cost $500 each and radio ads cost $100 each. If the company wants to buy a total of 220 ads, how many of each kind of ads should the company buy?

Let the number of a TV add be t, and of radio add be r.

30000 = 500.t + 100.r,

or dividing through by 100:

300 = 5.t + r.

But the total number of adds is to be 220, so:

220 = t + r.

So you now have a pair of simultaneous linear equations to solve.

Subtract the second from the first to get:

300 - 220 = (5.t + r) - (t + r),

simplify:

80 = 4.t,

or t=20, so r=200.

RonL

Thanks for your help on that word problem sorry about the double post Anymore help would be greatly appreciated.

Originally Posted by MathIlliterate

I am suppose to list variables and give equations. ...

5. A college student earned $8200 during summer vacation working as a waiter in a popular restaurant. The student invested part of the money at 8% and the rest at 7%. If the student received a total of $613 in interest at the end of the year. How much was invested at 8%?

...

Hello,

let x be the money invested at 8%
let y be the money invested at 7%

Then you get a pair of simultaneously equations:
x + y = 8200
0.08*x + 0.07*y = 613

For confirmation only: x = 3900; y = 4300

EB

Thanks for your help I am truly appreciative

Originally Posted by MathIlliterate

I am suppose to list variables and give equations. ...

6. A twin-engined aircraft can fly 816 mi. from city A to city B in 3 hrs. with the wind and make the return trip in 8 hrs. against the wind. What is the speed of the wind?[/B]

...

Hello,

the general formula to use is:


Let be and

You get a pair of two simultaneously equations:



Expand the RHS and rearrange. Solve for and

For confirmation only: v_a = 187 mph; v_w = 85 mph

EB

Originally Posted by MathIlliterate

I am suppose to list variables and give equations. ...


3. A chemist needs 110 milliters of a 31% solution but has only 10% and 43% solutions available. How many milliters of each should be mixed to get the desired solution?
...

Hello,

let x be the amount of the 10%-solution and
let y be the amount of the 43%-solution.

Then you get a pair of simultaneously equations:

x + y = 110
0.1*x + 0.43*y = 0.31*110

for confirmation only: x = 40; y = 70

EB

Originally Posted by MathIlliterate

I am suppose to list variables and give equations. ...


2. A charity sells tickets for a fundraising dinner. Each adult's ticket costs $10 and each child's ticket costs $5. A total of $1050 was raised by selling 130 tickets. How many of each kind of ticket was sold?

...

Hello,

let a be the number of adult's tickets and
let c be the number of child's tickets.

Then you get a pair of simultaneously equations:

a + c = 130
10*a + 5*c = 1030

For confirmation only: a = 76; c = 54

EB

Your the bomb earboth! I understand the break down of each word problem now. Thanks