# Please Need Help Fast World Problems

• December 13th 2006, 11:57 PM
MathIlliterate
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?

• December 14th 2006, 12:12 AM
CaptainBlack
Quote:

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 • December 14th 2006, 12:22 AM MathIlliterate Thank You Thanks for your help on that word problem sorry about the double post:o Anymore help would be greatly appreciated. • December 14th 2006, 12:29 AM earboth Quote: 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 • December 14th 2006, 12:35 AM MathIlliterate You Rock earboth! Thanks for your help I am truly appreciative:) • December 14th 2006, 12:39 AM earboth Quote: 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: $\text{way}=\text{speed} \cdot \text{time}$ Let be $v_a=\text{speed of airplane}$ and $v_w=\text{speed of wind}$ You get a pair of two simultaneously equations: $816=(v_a+v_w) \cdot 3$ $816=(v_a-v_w) \cdot 8$ Expand the RHS and rearrange. Solve for $v_a$ and $v_w$ For confirmation only: v_a = 187 mph; v_w = 85 mph EB • December 14th 2006, 12:44 AM earboth Quote: 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 • December 14th 2006, 12:47 AM earboth Quote: 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
• December 14th 2006, 12:55 AM
MathIlliterate
Thank You
Your the bomb earboth! I understand the break down of each word problem now. Thanks:D