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Writing Equations from Verbal Descriptions

Total questions: 8

Worksheet time: 4mins

Name
Class
Date
1.

For the school dance tickets are $3 for couples and $2 for singles. If 365 tickets were sold and the total receipts were $925, which pair of equations would determine the number of each ticket sold?

a)

xy=365x-y=365

3x+2y=9253x+2y=925

b)

xy=365x-y=365

x+y=925x+y=925

c)

3x+2y=3653x+2y=365

x+y=925x+y=925

d)

x+y=365x+y=365 3x+2y=9253x+2y=925

2.

Josiah currently has $2000 in his savings accounts. If the account earns 1.5% interest each year, which equation could he use to determine the total amount of money, yy , he will have after xx months?

a)

y=2000(1.5)xy=2000\left(1.5\right)^x

b)

y=2000(1.015)xy=2000\left(1.015\right)^x

c)

y=2000(1.15)xy=2000\left(1.15\right)^x

d)

y=2000(99.985)xy=2000\left(99.985\right)^x

3.

A certain rectangle has a perimeter of at least 50. Given ll represents the length of the rectangle and ww represents the width, select the inequality which represents this situation.

a)

2l+2w<502l+2w<50

b)

2l+2w502l+2w\le50

c)

2l+2w502l+2w\ge50

d)

l+w50l+w\ge50

4.

Muhammad went to the Hamburger Shack twice last week. On the first trip he bought 3 hamburgers and 4 orders of french fries for $7.10. On the second trip he bought only 2 hamburgers and an order of french fries for $3.40. Which system of equations best represents this situation if hh represents the cost of each hamburger and ff the cost of each order of french fries.

a)

3h+4f=7.103h+4f=7.10 2h+f=3.402h+f=3.40

b)

h+f=10h+f=10 5h+5f=10.505h+5f=10.50

c)

3h+4f=3.403h+4f=3.40 2h+f=7.102h+f=7.10

d)

3h+f=7.103h+f=7.10 2h+4f=3.402h+4f=3.40

5.

After a rainstorm, there are 2 m of water covering a road. The water decreases at a rate of 0.25m/h. Express the amount of water, ww , as a linear function of time, tt , in hours after the end of the rainstorm.

a)

w(t)=0.25t+2w\left(t\right)=0.25t+2

b)

w(t)=0.25t+2w\left(t\right)=-0.25t+2

c)

w(t)=0.25t2w\left(t\right)=0.25t-2

d)

w(t)=0.25t2w\left(t\right)=-0.25t-2

6.

A rectangle's length is 6 units longer than twice its width. If the width of the rectangle is 2x+32x+3 , what is the perimeter PP in terms of xx ?

a)

P=8x+12P=8x+12

b)

P=4x15P=4x-15

c)

P=12x+30P=12x+30

d)

P=12x8P=12x-8

7.

The current population of Middleton is 800 people. If the population is decreasing at a rate of 1.5% each year, which equation could be used to determine the town's population yy after xx years?

a)

y=800(1.03)xy=800\left(1.03\right)^x

b)

y=800(0.03)xy=800\left(0.03\right)^x

c)

y=800(1.97)xy=800\left(1.97\right)^x

d)

y=800(0.97)xy=800\left(0.97\right)^x

8.

A company manufactures two types of shoes, a dress shoe and a tennis shoe. The company decides that to make a profit they must manufacture at least 150 pairs of shoes. The dress shoes cost $85 a pair and the tennis shoes cost $50. If dd represents the number of dress shoes produced and tt represents the number of cheap shoes produced, which inequality represents this situation?

a)

d+t150d+t\le150

b)

d+t150d+t\ge150

c)

d+t<150d+t<150

d)

d+t>150d+t>150