Other Decimals - ACT Math
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Jenny is getting ready for school. She bought school supplies on a tax-free day. She bought notebooks for $1.25 each and crayons for $0.90 each. Jenny bought two more notebooks than crayons. She paid with a ten dollar bill and got $1.05 in change. How many notebooks did she buy?
Jenny is getting ready for school. She bought school supplies on a tax-free day. She bought notebooks for $1.25 each and crayons for $0.90 each. Jenny bought two more notebooks than crayons. She paid with a ten dollar bill and got $1.05 in change. How many notebooks did she buy?
Define variables as x = number of crayons and x + 2 = number of notebooks
To find out how much she spent, we subtract her change from what she paid with: 10.00 – 1.05 = 8.95
Then we need to solve the problem cost of notebooks plus the cost of crayons equals the total cost.
1.25(x + 2) + 0.90x = 8.95 and solving for x gives 3 crayons and 5 notebooks
Define variables as x = number of crayons and x + 2 = number of notebooks
To find out how much she spent, we subtract her change from what she paid with: 10.00 – 1.05 = 8.95
Then we need to solve the problem cost of notebooks plus the cost of crayons equals the total cost.
1.25(x + 2) + 0.90x = 8.95 and solving for x gives 3 crayons and 5 notebooks
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Simplify the following:
Simplify the following:
To add decimals, first add zeros to the necessary terms so they all have the same number of places to the right of the decimal point.
Now, temporarily drop the decimal and add the numbers as if they were whole numbers.
Finally, add the decimal place back in, in the same place you removed it from. In this case, we originally modified our numbers so they all had 3 numbers to the right of the decimal, so we will add the decimal back to the exact same place. Thus, our answer is:
To add decimals, first add zeros to the necessary terms so they all have the same number of places to the right of the decimal point.
Now, temporarily drop the decimal and add the numbers as if they were whole numbers.
Finally, add the decimal place back in, in the same place you removed it from. In this case, we originally modified our numbers so they all had 3 numbers to the right of the decimal, so we will add the decimal back to the exact same place. Thus, our answer is:
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Add: 
Add:
Rewrite the problem so that the tenths, hundredths, and thousandths digits align. Use zeros as placeholders and solve.
Rewrite the problem so that the tenths, hundredths, and thousandths digits align. Use zeros as placeholders and solve.
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If Exam 1 is worth 25% of the total grade, Exam 2 is worth 25% and Exam 3 is worth 50%, what is Dave’s final grade?
If Exam 1 is worth 25% of the total grade, Exam 2 is worth 25% and Exam 3 is worth 50%, what is Dave’s final grade?
Final Grade = Exam1 * 0.25 + Exam 2 * 0.25 + Exam3 * 0.50 =
96*0.25 + 70*0.25 + 85*0.5 =
24 + 17.5 + 42.5 = 84
Final Grade = Exam1 * 0.25 + Exam 2 * 0.25 + Exam3 * 0.50 =
96*0.25 + 70*0.25 + 85*0.5 =
24 + 17.5 + 42.5 = 84
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A car has gas mileage of 46 miles per gallon. Assume that gas costs $3.90 per gallon. What would be the total cost of gas if the car traveled 1,150 miles?
A car has gas mileage of 46 miles per gallon. Assume that gas costs $3.90 per gallon. What would be the total cost of gas if the car traveled 1,150 miles?
First find out how many gallons of gas the car consumed while traveling 1150 miles. This can be found out like so:
1150 miles x gallons/46 miles = 25 gallons
Multiplying 25 by $3.90 yields $97.50.
First find out how many gallons of gas the car consumed while traveling 1150 miles. This can be found out like so:
1150 miles x gallons/46 miles = 25 gallons
Multiplying 25 by $3.90 yields $97.50.
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A chemistry students needs to dilute some acid. How much water should be added to 2 L of 80% acid solution to yield 50% acid solution?
A chemistry students needs to dilute some acid. How much water should be added to 2 L of 80% acid solution to yield 50% acid solution?
Pure water would be 0% solution and pure solution would be 100%
V1P1 + V2P2 = VfPf
Let x = amount of water to add
x(0) + 2(0.80) = (x + 2)(0.50) which when solved gives x = 1.2 L
Pure water would be 0% solution and pure solution would be 100%
V1P1 + V2P2 = VfPf
Let x = amount of water to add
x(0) + 2(0.80) = (x + 2)(0.50) which when solved gives x = 1.2 L
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Kevin is looking at the blueprint of the house he is building. The scale is 1 inch = 5 feet. On paper, the master bedroom is 2.5 inches by 3 inches. What is the actual size of the bedroom?
Kevin is looking at the blueprint of the house he is building. The scale is 1 inch = 5 feet. On paper, the master bedroom is 2.5 inches by 3 inches. What is the actual size of the bedroom?
The given dimensions must be multiplied by 5, so 2.5 inches becomes 12.5 feet, and 3 inches becomes 15 feet.
The given dimensions must be multiplied by 5, so 2.5 inches becomes 12.5 feet, and 3 inches becomes 15 feet.
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Evaluate
Evaluate
First, 
Then, 
First,
Then,
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If 
, approximately how many inches are in one meter?
If
and 
Using the factor-label method we get the following equation.
We treat the units as if they are numbers, and can cancel the units from the fractions.
Using the factor-label method we get the following equation.
We treat the units as if they are numbers, and can cancel the units from the fractions.
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You bought a dozen eggs marked at 
and received 
change from 
. What is the percent of sales tax?
You bought a dozen eggs marked at
Set the equation up as
Solve for 
, which equals 
or
Therefore the percent sales tax is:
Set the equation up as
Solve for
or
Therefore the percent sales tax is:
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If Exam 1 is worth 25% of the total grade, Exam 2 is worth 25% and Exam 3 is worth 50%, what is Dave’s final grade?
If Exam 1 is worth 25% of the total grade, Exam 2 is worth 25% and Exam 3 is worth 50%, what is Dave’s final grade?
Final Grade = Exam1 * 0.25 + Exam 2 * 0.25 + Exam3 * 0.50 =
96*0.25 + 70*0.25 + 85*0.5 =
24 + 17.5 + 42.5 = 84
Final Grade = Exam1 * 0.25 + Exam 2 * 0.25 + Exam3 * 0.50 =
96*0.25 + 70*0.25 + 85*0.5 =
24 + 17.5 + 42.5 = 84
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A car has gas mileage of 46 miles per gallon. Assume that gas costs $3.90 per gallon. What would be the total cost of gas if the car traveled 1,150 miles?
A car has gas mileage of 46 miles per gallon. Assume that gas costs $3.90 per gallon. What would be the total cost of gas if the car traveled 1,150 miles?
First find out how many gallons of gas the car consumed while traveling 1150 miles. This can be found out like so:
1150 miles x gallons/46 miles = 25 gallons
Multiplying 25 by $3.90 yields $97.50.
First find out how many gallons of gas the car consumed while traveling 1150 miles. This can be found out like so:
1150 miles x gallons/46 miles = 25 gallons
Multiplying 25 by $3.90 yields $97.50.
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A chemistry students needs to dilute some acid. How much water should be added to 2 L of 80% acid solution to yield 50% acid solution?
A chemistry students needs to dilute some acid. How much water should be added to 2 L of 80% acid solution to yield 50% acid solution?
Pure water would be 0% solution and pure solution would be 100%
V1P1 + V2P2 = VfPf
Let x = amount of water to add
x(0) + 2(0.80) = (x + 2)(0.50) which when solved gives x = 1.2 L
Pure water would be 0% solution and pure solution would be 100%
V1P1 + V2P2 = VfPf
Let x = amount of water to add
x(0) + 2(0.80) = (x + 2)(0.50) which when solved gives x = 1.2 L
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Kevin is looking at the blueprint of the house he is building. The scale is 1 inch = 5 feet. On paper, the master bedroom is 2.5 inches by 3 inches. What is the actual size of the bedroom?
Kevin is looking at the blueprint of the house he is building. The scale is 1 inch = 5 feet. On paper, the master bedroom is 2.5 inches by 3 inches. What is the actual size of the bedroom?
The given dimensions must be multiplied by 5, so 2.5 inches becomes 12.5 feet, and 3 inches becomes 15 feet.
The given dimensions must be multiplied by 5, so 2.5 inches becomes 12.5 feet, and 3 inches becomes 15 feet.
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Evaluate
Evaluate
First,
Then,
First,
Then,
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If , approximately how many inches are in one meter?
If
and
Using the factor-label method we get the following equation.
We treat the units as if they are numbers, and can cancel the units from the fractions.
Using the factor-label method we get the following equation.
We treat the units as if they are numbers, and can cancel the units from the fractions.
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You bought a dozen eggs marked at and received change from . What is the percent of sales tax?
You bought a dozen eggs marked at
Set the equation up as
Solve for , which equals
or
Therefore the percent sales tax is:
Set the equation up as
Solve for
or
Therefore the percent sales tax is:
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What is 
?
What is
0.625 is equal to 
, while .25 is equal to 
. Dividing by fractions is the same as multiplying by the reciprocal of the divisor. Thus, 
which equals 
, which simplifies to 2.5.
0.625 is equal to
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Divide: 
Divide:
Eliminate the decimal place on the denominator by moving the decimal place 2 spaces to the right. Follow suit for the numerator. The decimal place should also move the same number of units to the right. Evaluate.
Eliminate the decimal place on the denominator by moving the decimal place 2 spaces to the right. Follow suit for the numerator. The decimal place should also move the same number of units to the right. Evaluate.
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Divide: 
Divide:
Rewrite 
so that both are in fraction form.
Convert the division sign to multiplication, and take the reciprocal of the 2nd term.
Rewrite
Convert the division sign to multiplication, and take the reciprocal of the 2nd term.
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