הֶסבֵּר:
This is an inverse ratio problem.
1/x = 1/a + 1/b where a is the time Sally can paint a house, b is the time John can paint a house, and x is the time Sally and John can together paint a house.
So,
1/x = 1/4 + 1/6 … We use the least common multiple in the denominator that is 24:
1/x = 6/24 + 4/24
1/x = 10/24
x = 24/10
x = 2.4 hours.
In other words; 2 hours + 0.4 hours = 2 hours + 0.4•60 minutes
= 2 hours 24 minutes
הֶסבֵּר:
We check the fractions taking place in the question. We see that there is a “half” (that is 1/2) and 3/7. So, we multiply the denominators of these fractions to decide how to name the total money. We say that Mr. Johnson has 14x at the beginning; he gives half of this, meaning 7x, to his family. $250 to his landlord. He has 3/7 of his money left. 3/7 of 14x is equal to:
14x * (3/7) = 6x
So,
Spent money is: 7x + 250
Unspent money is: 6×51
Total money is: 14x
Write an equation: total money = spent money + unspent money
14x = 7x + 250 + 6x
14x – 7x – 6x = 250
x = 250
We are asked to find the total money that is 14x:
14x = 14 * 250 = $3500
הֶסבֵּר:
My age: x
My brother is 3 years older than me: x + 3
My father is 3 less than 2 times my age: 2x – 3
My father’s age divided by 5 is equal to my brother’s age divided by 3: (2x – 3) / 5 = (x + 3) / 3
By cross multiplication:
5(x + 3) = 3(2x – 3)
5x + 15 = 6x – 9
x = 24
My father’s age: 2.24 – 3= 48 – 3 = 45
הֶסבֵּר:
The original price of the dishwasher is $450. During a 15% off sale, the price of the dishwasher will be reduced by:
15% of $450 = 0.15 x $450 = $67.50
So the sale price of the dishwasher will be:
$450 – $67.50 = $382.50
As an employee, the person receives an additional 20% off the lowest price, which is $382.50. We can calculate the additional discount as:
20% of $382.50 = 0.20 x $382.50 = $76.50
So the final price that the employee will pay for the dishwasher is:
$382.50 – $76.50 = $306.00
הֶסבֵּר:
This is a simple direct proportion problem:
If Lynn can type 1 page in p minutes, then she can type x pages in 5 minutes
We do cross multiplication: x * p = 5 * 1
Then, x = 5/p
הֶסבֵּר:
The first time, Brian answered 150 questions correctly and the second time he answered 30% more correctly, so,
150 + (30/100 * 150) ; 30% of 150 = 45, or (30 * 150)/100
so 150 + 45 = 195
הֶסבֵּר:
Original price = x,
80/100 = 12590/X,
80X = 1259000,
X = 15,737.50
הֶסבֵּר:
First calculate total square feet, which is 15 * 24 = 360 ft2. Next, convert this value to square yards, (1 yards2 = 9 ft2) which is 360/9 = 40 yards2. At $0.50 per square yard, the total cost is 40 * 0.50 = $20.
הֶסבֵּר:
The ratio between black and blue pens is 7 to 28 or 7:28. Bring to the lowest terms by dividing both sides by 7 gives 1:4.
הֶסבֵּר:
We are given that each of the n employees earns s amount of salary weekly. This means that one employee earns s salary weekly. So; Richard has ‘ns’ amount of money to employ n employees for a week.
We are asked to find the number of days n employees can be employed with x amount of money. We can do simple direct proportion:
If Richard can employ n employees for 7 days with ‘ns’ amount of money, Richard can employ n employees for y days with x amount of money … y is the number of days we need to find.
We can do cross multiplication:
y = (x * 7)/(ns)
y = 7x/ns
הֶסבֵּר:
At 100% efficiency, 1 machine produces 1450/10 = 145 m of cloth.
At 95% efficiency, 4 machines produce 4 * 145 * 95/100 = 551 m of cloth.
At 90% efficiency, 6 machines produce 6 * 145 * 90/100 = 783 m of cloth.
Total cloth produced by all 10 machines = 551 + 783 = 1334 m
Since the information provided and the question are based on 8 hours, we did not need to use time to reach the answer.
