1. A two digit number is three less than seven times the sum of its digits. if the digits are reversed, the new number is 18 less than the original number. what is the new number?
2. The numerator a fraction is 3 less than the denominator. If 5 is added to both the numerator and denominator, the value of the resulting fractin is 3/4. Find the original fraction.
3. The difference between the first and second number is 0. Find the numbers such that the difference between thrice the first and twice the second is 18.
4. A theater show charges 60 for adults and 48 for seniors. On a day when 310 people paid an admission, the total receipts were 18,192. How many who paid were adults? How many were seniors.
Hi! Can you also give me tips on how to solve word problems. Am having a hard time. Thanks.
4. Let x = seniors and y = adults
y = 310 - x
60y + 48x = 18,192
Substitute 310-x for y in second equation and solve for x. Insert that value into the first equation and solve for y. Check by inserting both values into the second equation.
1. new number is 35
Let x is digit in 10th place and y be in unit place of original number. and the original number is 10x+y
iven 10x+y=7(x+y)-3
Thus we get 3x-6y=-3 ......(i)
The reverse of original number is 10y+x
Also given 10y+x=10x+y-18,
that is 9x-9y=18 ......(ii)
solving (i) and (ii)get x=5 and y=3.
That is the original number is 53 and new number is 35
2. Let x be the numerator and y be the denominator.
Given x = y - 3
Also (x + 5)/ (y + 5) = 3/4
Substitute x = y - 3 in the above equation we get (y + 2) / (y + 5) = 3/4
Cross multiply this we get y = 7 and substitute y in first equation gives x = 4
Thus the fraction is 4/7
Sure! I'd be happy to help you solve these word problems and give you some tips along the way.
1. Let's break down the problem step by step:
- Let's assume the tens digit of the number is 'a' and the ones digit is 'b'.
- The two-digit number can be represented as 10a + b.
- According to the problem, 10a + b = 7(a + b) - 3.
- Simplifying this equation, we get 3a = 6b - 3.
- Rearranging the equation, we have a = 2b - 1.
- The new number obtained by reversing the digits is 10b + a.
- It is given that 10b + a = 10a + b - 18.
To find the new number:
- Substitute the value of 'a' from the first equation into the second equation.
- Solve for 'b' to find the ones digit.
- Once you have 'b', substitute it back into the first equation to find 'a'.
- Finally, find the new number by substituting the values of 'a' and 'b' into the equation 10b + a.
2. Let's solve this problem step by step:
- Let's assume the original fraction is a/b.
- According to the problem, a = b - 3.
- If 5 is added to both the numerator and denominator, the resulting fraction becomes (a + 5)/(b + 5), and its value is 3/4.
- So, we have (a + 5)/(b + 5) = 3/4.
To find the original fraction:
- Substitute the value of 'a' from the first equation into the second equation.
- Solve for 'b' to find the denominator.
- Once you have 'b', find the numerator using the equation a = b - 3.
- Finally, the original fraction is a/b.
3. Let's break down the problem step by step:
- Let's assume the first number is 'x' and the second number is 'y'.
- According to the problem, x - y = 0.
- The difference between thrice the first number and twice the second number is 18, so 3x - 2y = 18.
To find the numbers:
- Since x - y = 0, we can say that x = y.
- Substitute the value of 'y' into the second equation to find 'x'.
- Once you find 'x', you can find 'y' as well since they are the same.
- So, the numbers are x and y, where x = y.
4. Let's solve this problem step by step:
- Let's assume the number of adults is 'x' and the number of seniors is 'y'.
- According to the problem, the price for adults is $60 and the price for seniors is $48.
- The total number of people who paid an admission is 310, so x + y = 310.
- The total receipts were $18,192, so 60x + 48y = 18,192.
To find the number of adults and seniors:
- Solve the system of equations formed by x + y = 310 and 60x + 48y = 18,192.
- You can solve the system using various methods such as substitution, elimination, or matrices.
- Once you find the values of 'x' and 'y', you'll know the number of adults and seniors.
Tips for solving word problems:
1. Read the problem carefully, paying attention to all the given information.
2. Underline or highlight the important details and variables.
3. Define variables to represent unknown quantities.
4. Break down the problem into smaller steps or equations.
5. Translate the given information into mathematical equations.
6. Solve the equations to find the unknown values.
7. Check if the answer makes sense in the context of the problem.
8. Practice solving various types of word problems to improve your problem-solving skills.
I hope these explanations and tips help you solve the word problems! Let me know if you have any further questions.