Answer: Tine solved 15 hard puzzles.
Step-by-step explanation:
Let x be the number of easy puzzles and y be the number of hard puzzels.
Given : A player earns 30 points for solving an easy puzzles and 60 points for solving a hard puzzled.
Tina solved a total of 50 Puzzles playing this game, earning 1950 points in all.
Then system of equations for above description:
[tex]x+y=50--------(1)\\30x+60y=1950---------(2)[/tex]
Multiply 60 in equation (1), we get
[tex]60x+60y=3000-----(3)[/tex]
Subtract equation (2) from (3), we get
[tex]30x=1050\\\\\Rightarrow\ x=\dfrac{1050}{30}=35[/tex]
Put x=-35 in (1), we get
[tex]35+y=50\\\\\Rightarrow\ y=50-35=15[/tex]
Hence, Tine solved 15 hard puzzles.
Using a system of equations, it is found that Tina solved 35 easy puzzles and 15 hard puzzles.
For our system, we are going to say that:
x is the number of easy puzzles solved.y is the number of hard puzzles solved.Total of 50 puzzles, thus:
[tex]x + y = 50[/tex]
Each easy puzzle earns 30 points, each hard 60, total of 1950 points, thus:
[tex]30x + 60y = 1950[/tex]
From the first equation:
[tex]x = 50 - y[/tex]
Replacing in the second:
[tex]30x + 60y = 1950[/tex]
[tex]30(50 - y) + 60y = 1950[/tex]
[tex]30y = 450[/tex]
[tex]y = \frac{450}{30}[/tex]
[tex]y = 15[/tex]
Then:
[tex]x = 50 - y = 50 - 15 = 35[/tex]
Tina solved 35 easy puzzles and 15 hard puzzles.
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Me. Driscoll has 9 reports to grade. There are 6 page for each report. He grades 12 pages. How many pages does he still have to grade?
The students at Porterville Elementary sold raffle tickets, each for the same price, for a fundraiser. The equation below shows how much money was raised with t tickets sold. $966 = $14t
Find sum or difference.
1/6 + 3/8
A. 4/6
B. 4/8
C. 4/14
D. 13/24
find common denominator:
6*4 =24, 8*3 = 24
1/6 = 4/24
3/8 = 9/24
4/24 + 9/24 = 13/24
Answer is D
Denny rode his bicycle miles in the morning. Then he rode miles in the afternoon. How far did he ride his bicycle altogether?
Karen wants to buy a $22.50 jacket that is marked 20% off. Select from the drop-down menu to correctly complete the sentence. The best estimate for the discount can be found using the expression
discount = price times % off
discount = 22.50 x 0.20
discount = $4.50
Answer:
[tex]\$22.50*0.20=\$4.50[/tex]
Step-by-step explanation:
Let
x-------> original price
y------> percentage of discount
z-----> discount
we know that
[tex]z=xy[/tex]
In this problem we have
[tex]x=\$22.50[/tex]
[tex]y=20\%=\frac{20}{100}=0.20[/tex]
Substitute the values
[tex]z=\$22.50*0.20=\$4.50[/tex]
what is the simplified value of 40+2⋅3−2 and 40+2⋅3−2 and 9+32−1⋅4
On two tests so far this year, a student received a 78 and a 93. The student wants an average between 80 and 90 inclusive. What are all of the possible scores for the third test so that the student falls within this average?
How many 3/4 cup servings are in 1/2 of a cup of milk? Write your answer in simplest form.
The number of 3/4 cup servings that are in 1/2 of a cup of milk is [tex]\frac{2}{3}[/tex]
In order to determine the number of 3/4 cup servings that are in 1/2 cup of milk, divide the fraction of the cup of milk by the fraction of cup servings
Cup of milk ÷ Number of cup servings
= [tex]\frac{1}{2}[/tex] ÷ [tex]\frac{3}{4}[/tex]
[tex]\frac{1}{2}[/tex] x [tex]\frac{4}{3}[/tex]
= [tex]\frac{4}{6}[/tex]
In order to express the answer in its simplest form, divide the numerator by two and the denominator by 2. The numerator and the denominator are both divided by two because two is a common factor of 4 and 6
= [tex]\frac{2}{3}[/tex]
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The dance committee has 1036 flowers.They want to divide the flowers evenly among 28 centerpieces.How many flowers will be in each centerpiece? A 28 B 34 C 37 D 40
Dev knows he only has 8 gallons of gasoline in the tank he wants to go on a 300-mile trip will he have to buy more gasoline?
How do you turn percents into fractions?
Step 1: You want to remove the percent sign and then put the number over 100.
Step 2: If the percent is not a whole number then you want to multiply the top and bottom number by 10 but only for every number that comes after the decimal point.
Step 3: Always simplify if possible.
Examples:
43% = [tex]\frac{43}{100}[/tex]
78% = [tex]\frac{78}{100}[/tex] = [tex]\frac{39}{50}[/tex]
0.4% = [tex]\frac{0.4}{100}[/tex] = [tex]\frac{4}{1000}[/tex] = [tex]\frac{1}{250}[/tex]
Converting percents to fractions involves writing the percent as a fraction with a denominator of 100 and then simplifying. For example, 75% is equivalent to 75/100, which simplifies to 3/4. Decimals can be converted to percents by multiplying by 100 and adding the percent sign.
Converting Percents to Fractions
To convert a percent to a fraction, start by writing the percent value as a fraction with a denominator of 100. For example, 75% would be written as 75/100. The next step is to simplify the fraction if possible. To simplify, you find the greatest common divisor (GCD) of the numerator and the denominator and divide both by this number. For instance, the GCD of 75 and 100 is 25, so when we divide both the numerator and the denominator by 25, we get 3/4. Hence, 75% as a fraction in simplest terms is 3/4.
When converting to decimals, simply divide the numerator by the denominator. So, 75% becomes 0.75 when turned into a decimal. Conversely, to convert a decimal to a percent, you multiply by 100 and add the percent symbol (%). For instance, converting the decimal 0.75 to a percent, you would calculate 0.75 * 100 which equals 75%, completing the conversion.
Calculating percents is about understanding the ratio or fraction that the percent represents. The term 'percent' literally means 'per hundred', so any percent can be thought of as that number over 100. For example, 3% means 3/100 and 100% represents a whole or 1 as it's equivalent to 100/100.
What is 5 units away from (-1, -2)
Answer:
Step-by-step explanation:
There's a whole family of points.
(x + 1)^2 + (y + 2)^2= 25
The above is an equation that represents a circle.
Three points are marked below 2 of which are easily seen to be 5 units away from the center (-1,-2)
Which diagram does not result in the expression 4x+4
Multiply: 2 4/5 x -5 2/3
Please help me please. What is the slope of a line perpendicular to the line whose equation is 5x-2y=11?
What is the value of expression? 57.8 x 64 HELP PLEASE ASAP
Haruka hiked several kilometers in the morning in the morning. She only hiked 6 kilometers in the afternoon, which was 25% less she had hiked in the morning. How many kilometers did haruka hike in all?
The complete distance Haruka hiked can be calculated by converting the percent to decimal.
The total distance is 14 km Haruka hike in all.
Given:
She hiked in afternoon is [tex]6\: \rm km[/tex].
Let the distance hiked in morning is [tex]x[/tex].
As per the question, 6 kilometers 25% less she had hiked in morning.[tex]\begin{aligned}\left(\dfrac{100\%-25\%}{100}\right)x&=6\\0.75x&=6\\x&=\dfrac{6}{0.75}\\x&=8\\\end[/tex]
Therefore, Haruka hiked [tex]8\:\rm km[/tex] in morning.
Calculate the total distance hiked.
[tex]\rm Total\: distance=8+6=14 \:\rm km[/tex]
Thus, the total distance is 14 Km Haruka hike in all.
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what is -3x + b = 6x . Solve for x
Perform the following calculation: (–16) – (–42)
What is the sum of -7/18 and -3/6
a.) -4/9
b.) - 8/9
c.) 4/9
d.) 8/9
Answer:
-b) -8/9
Step-by-step explanation:
Answer:
The correct Answer is B.) -8/9
Step-by-step explanation:
HAVE AN AMAZING DAY!!
from 91 books to 145 books
find the percent increase. round to the nearest percent.
Which expression equals -(9x + 8) - 2(x -5)
Simplify and express the answer as a decimal. (−3+6) 2 ÷4.5
-2(v+5)-4v
use the distributive property to simplify.
PLS help!
If a 25 foot tall tree cast a 15 foot shadow, what is the height of a tree if it’s shadow is 6 feet long
set this up as a ratio
25 ft tree / 15 foot shadow = X ft tree / 6 foot shadow
25/15 = X/6
cross multiply:
150 / 15x
x = 150/15 = 10
the tree is 10 feet tall
In 2007, the population of North America was approximately 5.15 x 10^8 people and the population of South America was approximately 3.04 x 10^8 people. What is the combined population of North and South America for this year?
A) 8.19 x 10^16 people
B) 8.19 x 10^9 people
C) 8.19 x 10^8 people
D) 8.19 x 10^64 people
A passenger train has 15 cars that each hold the same number of passengers. The train is filled with 1,020 passengers. How many passengers does each car hold?
Enter M for multiplication or D for division.
factor out the coefficient of the variable 1/4 y + 3/8
is xy=6 a linear equation
The currency in Argentina is the Peso. The exchange rate is approximately $3 = 1 Peso. At this rate, how many Pesos would you get if you exchanged $121.10?
The Pesos you would get if you exchanged $121.10 using an exchange rate of $3 = 1 Peso, you can set up a proportion and solve for x.
Explanation:To calculate how many Pesos you would get if you exchanged $121.10 at an exchange rate of $3 = 1 Peso, you can set up a proportion:
$3 / 1 Peso = $121.10 / x Pesos
Cross multiply to solve for x:
$3 * x = $121.10 * 1
x = $363.30
Therefore, you would get 363.30 Pesos if you exchanged $121.10 at the given exchange rate.
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