I need help with these three problems. I cant figure them out.
3. The difference of two numbers is tripled. The result is decreased by 1. If the lesser of the two numbers is 4 the result is 8.3. Find the greater number.
4. A number increased by 21 is ewuivalent to half the number increased by 18.5. find the number.
11. Kerry comutes 60 mi per day. If she drives 30 mi/h during the morning rush and returns over the same route at 50 mi/h how much time does she typically spend commuting each day.
Please help me and thank you very much!
First set up problems to solve each one assiging variables to each unknown. Remember, you need the same number of problems as you have variables.
Convert the words into one or more mathematical equations. I'll get you going on the first one.
"The difference of two numbers ..."
x - y
"... is tripled."
(x - y) * 3
or equivalently
3(x - y)
"The result is decreased by 1."
3(x - y) - 1
"If the lesser of the two numbers is 4 ..."
y = 4, so we have
3(x - 4) - 1
"the result is 8.3."
3(x - 4) - 1 = 8.3
"Find the greater number. "
solve the above for x.
I'd be happy to help you with these problems! Let's tackle them one at a time:
Problem 3:
We are given that the difference of two numbers is tripled and then decreased by 1, resulting in 8.3 when the lesser number is 4. Let's denote the two numbers as x and y, where x is the lesser number and y is the greater number.
The first equation we can form is: 3(x - y) - 1 = 8.3. This equation represents the fact that the difference of the two numbers is tripled and decreased by 1.
We are also given that x = 4. Substituting this value in the equation, we get: 3(4 - y) - 1 = 8.3.
Now, let's solve for y. Start by simplifying the equation: 12 - 3y - 1 = 8.3.
Combine like terms: -3y + 11 = 8.3.
Subtract 11 from both sides: -3y = -2.7.
Divide both sides by -3: y = 0.9.
So, the greater number is 0.9.
Problem 4:
We are given that a number increased by 21 is equivalent to half the number increased by 18.5. Let's denote the number as x.
The equation we can form is: x + 21 = (1/2)(x + 18.5).
Now, let's solve for x. Start by simplifying the equation: x + 21 = (1/2)x + 9.25.
Subtract (1/2)x from both sides: (1/2)x - x + 21 = 9.25.
Combine like terms: (1/2)x - (2/2)x + 21 = 9.25.
Simplify the equation: (-1/2)x + 21 = 9.25.
Subtract 21 from both sides: (-1/2)x = -11.75.
Divide both sides by (-1/2): x = 23.5.
So, the number is 23.5.
Problem 11:
We are given that Kerry commutes 60 miles per day. During the morning rush, she drives at 30 mi/h, and on her return, she drives at 50 mi/h. We want to find the time she typically spends commuting each day.
Let's assume she spends x hours driving during the morning rush. So, her driving time on the return trip would be (60 - x) hours, as the total driving time is 60 miles.
To find the time, we use the formula: Time = Distance / Speed. In this case, distance is 60 miles, and speed is 30 mi/h or 50 mi/h.
For the morning rush, we can write the equation: x = 60 miles / 30 mi/h.
Simplify the equation: x = 2 hours.
For the return trip, we can write the equation: (60 - x) = 60 miles / 50 mi/h.
Simplify the equation: 60 - x = 1.2 hours.
Now, let's find the total time by adding the morning rush and return trip times: Total time = x + (60 - x) = 2 + 1.2 = 3.2 hours.
So, Kerry typically spends 3.2 hours commuting each day.
I hope this helps! Let me know if you have any further questions.