# 1.10 Systems of measurement  (Page 2/13)

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## Make unit conversions.

1. Multiply the measurement to be converted by 1; write 1 as a fraction relating the units given and the units needed.
2. Multiply.
3. Simplify the fraction.
4. Simplify.

When we use the identity property of multiplication to convert units, we need to make sure the units we want to change from will divide out. Usually this means we want the conversion fraction to have those units in the denominator.

Ndula, an elephant at the San Diego Safari Park, weighs almost 3.2 tons. Convert her weight to pounds.

## Solution

We will convert 3.2 tons into pounds. We will use the identity property of multiplication, writing 1 as the fraction $\frac{2000\phantom{\rule{0.2em}{0ex}}\text{pounds}}{1\phantom{\rule{0.2em}{0ex}}\text{ton}}.$

 $\text{3.2 tons}$ Multiply the measurement to be converted, by 1. $\text{3.2 tons}\cdot 1$ Write 1 as a fraction relating tons and pounds. $\text{3.2 tons}\cdot \frac{\text{2,000 pounds}}{\text{1 ton}}$ Simplify. Multiply. $\text{6,400 pounds}$ Ndula weighs almost 6,400 pounds.

Arnold’s SUV weighs about 4.3 tons. Convert the weight to pounds.

8,600 pounds

The Carnival Destiny cruise ship weighs 51,000 tons. Convert the weight to pounds.

102,000,000 pounds

Sometimes, to convert from one unit to another, we may need to use several other units in between, so we will need to multiply several fractions.

Juliet is going with her family to their summer home. She will be away from her boyfriend for 9 weeks. Convert the time to minutes.

## Solution

To convert weeks into minutes we will convert weeks into days, days into hours, and then hours into minutes. To do this we will multiply by conversion factors of 1.

 9 weeks Write $1$ as $\frac{\text{7 days}}{\text{1 week}}$ , $\frac{\text{24 hours}}{\text{1 day}}$ , and $\frac{\text{60 minutes}}{\text{1 hour}}$ . $\frac{\text{9 wk}}{1}\cdot \frac{\text{7 days}}{\text{1 wk}}\cdot \frac{\text{24 hr}}{\text{1 day}}\cdot \frac{\text{60 min}}{\text{1 hr}}$ Divide out the common units. Multiply. $\frac{9\cdot 7\cdot 24\cdot \text{60 min}}{1\cdot 1\cdot 1\cdot 1}$ Multiply. $\text{90,720 min}$

Juliet and her boyfriend will be apart for 90,720 minutes (although it may seem like an eternity!).

The distance between the earth and the moon is about 250,000 miles. Convert this length to yards.

440,000,000 yards

The astronauts of Expedition 28 on the International Space Station spend 15 weeks in space. Convert the time to minutes.

151,200 minutes

How many ounces are in 1 gallon?

## Solution

We will convert gallons to ounces by multiplying by several conversion factors. Refer to [link] .

 1 gallon Multiply the measurement to be converted by 1. $\frac{\text{1 gallon}}{1}\cdot \frac{\text{4 quarts}}{\text{1 gallon}}\cdot \frac{\text{2 pints}}{\text{1 quart}}\cdot \frac{\text{2 cups}}{\text{1 pint}}\cdot \frac{\text{8 ounces}}{\text{1 cup}}$ Use conversion factors to get to the right unit. Simplify. Multiply. $\frac{1\cdot 4\cdot 2\cdot 2\cdot \text{8 ounces}}{1\cdot 1\cdot 1\cdot 1\cdot 1}$ Simplify. $\text{128 ounces}$ There are 128 ounces in a gallon.

How many cups are in 1 gallon?

16 cups

How many teaspoons are in 1 cup?

48 teaspoons

## Use mixed units of measurement in the u.s. system

We often use mixed units of measurement in everyday situations. Suppose Joe is 5 feet 10 inches tall, stays at work for 7 hours and 45 minutes, and then eats a 1 pound 2 ounce steak for dinner—all these measurements have mixed units.

Performing arithmetic operations on measurements with mixed units of measures requires care. Be sure to add or subtract like units!

Seymour bought three steaks for a barbecue. Their weights were 14 ounces, 1 pound 2 ounces and 1 pound 6 ounces. How many total pounds of steak did he buy?

## Solution

We will add the weights of the steaks to find the total weight of the steaks.

 Add the ounces. Then add the pounds. Convert 22 ounces to pounds and ounces. $\phantom{\rule{0.35em}{0ex}}$ 2 pounds + 1 pound, 6 ounces Add the pounds. $\phantom{\rule{0.35em}{0ex}}$ 3 pounds, 6 ounces Seymour bought 3 pounds 6 ounces of steak.

-65r to the 4th power-50r cubed-15r squared+8r+23 ÷ 5r
write in this form a/b answer should be in the simplest form 5%
convert to decimal 9/11
August
Equation in the form of a pending point y+2=1/6(×-4)
write in simplest form 3 4/2
August
From Google: The quadratic formula, , is used in algebra to solve quadratic equations (polynomial equations of the second degree). The general form of a quadratic equation is , where x represents a variable, and a, b, and c are constants, with . A quadratic equation has two solutions, called roots.
Melissa
what is the answer of w-2.6=7.55
10.15
Michael
w = 10.15 You add 2.6 to both sides and then solve for w (-2.6 zeros out on the left and leaves you with w= 7.55 + 2.6)
Korin
Nataly is considering two job offers. The first job would pay her $83,000 per year. The second would pay her$66,500 plus 15% of her total sales. What would her total sales need to be for her salary on the second offer be higher than the first?
x > $110,000 bruce greater than$110,000
Michael
Estelle is making 30 pounds of fruit salad from strawberries and blueberries. Strawberries cost $1.80 per pound, and blueberries cost$4.50 per pound. If Estelle wants the fruit salad to cost her $2.52 per pound, how many pounds of each berry should she use? nawal Reply$1.38 worth of strawberries + $1.14 worth of blueberries which=$2.52
Leitha
how
Zaione
is it right😊
Leitha
lol maybe
Robinson
8 pound of blueberries and 22 pounds of strawberries
Melissa
8 pounds x 4.5 = 36 22 pounds x 1.80 = 39.60 36 + 39.60 = 75.60 75.60 / 30 = average 2.52 per pound
Melissa
8 pounds x 4.5 equal 36 22 pounds x 1.80 equal 39.60 36 + 39.60 equal 75.60 75.60 / 30 equal average 2.52 per pound
Melissa
hmmmm...... ?
Robinson
8 pounds x 4.5 = 36 22 pounds x 1.80 = 39.60 36 + 39.60 = 75.60 75.60 / 30 = average 2.52 per pound
Melissa
The question asks how many pounds of each in order for her to have an average cost of $2.52. She needs 30 lb in all so 30 pounds times$2.52 equals $75.60. that's how much money she is spending on the fruit. That means she would need 8 pounds of blueberries and 22 lbs of strawberries to equal 75.60 Melissa good Robinson 👍 Leitha thanks Melissa. Leitha nawal let's do another😊 Leitha we can't use emojis...I see now Leitha Sorry for the multi post. My phone glitches. Melissa Vina has$4.70 in quarters, dimes and nickels in her purse. She has eight more dimes than quarters and six more nickels than quarters. How many of each coin does she have?
10 quarters 16 dimes 12 nickels
Leitha
A private jet can fly 1,210 miles against a 25 mph headwind in the same amount of time it can fly 1,694 miles with a 25 mph tailwind. Find the speed of the jet.
wtf. is a tail wind or headwind?
Robert
48 miles per hour with headwind and 68 miles per hour with tailwind
Leitha
average speed is 58 mph
Leitha
Into the wind (headwind), 125 mph; with wind (tailwind), 175 mph. Use time (t) = distance (d) ÷ rate (r). since t is equal both problems, then 1210/(x-25) = 1694/(×+25). solve for x gives x=150.
bruce
the jet will fly 9.68 hours to cover either distance
bruce
Riley is planning to plant a lawn in his yard. He will need 9 pounds of grass seed. He wants to mix Bermuda seed that costs $4.80 per pound with Fescue seed that costs$3.50 per pound. How much of each seed should he buy so that the overall cost will be $4.02 per pound? Vonna Reply 33.336 Robinson Amber wants to put tiles on the backsplash of her kitchen counters. She will need 36 square feet of tiles. She will use basic tiles that cost$8 per square foot and decorator tiles that cost $20 per square foot. How many square feet of each tile should she use so that the overall cost of the backsplash will be$10 per square foot?
Ivan has $8.75 in nickels and quarters in his desk drawer. The number of nickels is twice the number of quarters. How many coins of each type does he have? mikayla Reply 2q=n ((2q).05) + ((q).25) = 8.75 .1q + .25q = 8.75 .35q = 8.75 q = 25 quarters 2(q) 2 (25) = 50 nickles Answer check 25 x .25 = 6.25 50 x .05 = 2.50 6.25 + 2.50 = 8.75 Melissa John has$175 in $5 and$10 bills in his drawer. The number of $5 bills is three times the number of$10 bills. How many of each are in the drawer?
7-$10 21-$5
Robert
Enrique borrowed $23,500 to buy a car. He pays his uncle 2% interest on the$4,500 he borrowed from him, and he pays the bank 11.5% interest on the rest. What average interest rate does he pay on the total \$23,500? (Round your answer to the nearest tenth of a percent.)
Two sisters like to compete on their bike rides. Tamara can go 4 mph faster than her sister, Samantha. If it takes Samantha 1 hour longer than Tamara to go 80 miles, how fast can Samantha ride her bike?
8mph
michele
16mph
Robert
3.8 mph
Ped
16 goes into 80 5times while 20 goes into 80 4times and is 4mph faster
Robert
help me understand graphs