Example Question - richard and tom's age
Here are examples of questions we've helped users solve.
Age Problem Solution with Algebra
The image contains a math word problem that reads: "Richard and Tom have a combined age of 49. Richard is 3 years older than twice Tom's age. How old are Richard and Tom?" Let's use algebra to solve this problem. We'll let R represent Richard's age and T represent Tom's age. We have two pieces of information: 1. Combined age: R + T = 49 2. Richard's age in relation to Tom's age: R = 3 + 2T Now we have two equations: (1) R + T = 49 (2) R = 3 + 2T We can substitute the value of R from equation (2) into equation (1): 3 + 2T + T = 49 Now combine like terms: 3 + 3T = 49 Subtract 3 from both sides to solve for T: 3T = 49 - 3 3T = 46 Now divide by 3 to get T: T = 46 / 3 T = 15⅓ However, ages are typically represented in whole numbers so the age should not be a fraction. Let's check our calculation to avoid any fraction since the question probably expects whole numbers as an answer. Dividing 46 by 3 again, T = 46 / 3 T = 15 with a remainder of 1. This means that Tom's age is 15, not 15⅓. Now we can find Richard's age by substituting T back into equation (2): R = 3 + 2(15) R = 3 + 30 R = 33 So, Richard is 33 years old and Tom is 15 years old.
Age Word Problem Solution
The image contains a word problem that states: "Richard and Tom have a combined age of 49. Richard is 3 years older than twice Tom's age. How old are Richard and Tom?" We can turn this word problem into a system of equations with two variables, R for Richard's age and T for Tom's age. The first equation comes from the first sentence: R + T = 49 (Equation 1) The second sentence provides us with a second equation: R = 2T + 3 (Equation 2) With these two equations, we can solve for R and T. We can use the substitution method by substituting Equation 2 into Equation 1: (2T + 3) + T = 49 Just simplify and solve for T: 2T + T = 49 - 3 3T = 46 T = 46 / 3 T = 15.333... Since we are typically dealing with whole years for ages, rounding down to the nearest whole number wouldn't be conventionally correct for determining age, but it seems the question might have assumed whole numbers, so let's consider T as 15 for the purposes of this problem (though in real-world terms, the exact age could also be a fractional part of a year). Now we will solve for R using T = 15: R = 2(15) + 3 R = 30 + 3 R = 33 Therefore, Tom is 15 years old, and Richard is 33 years old.
CamTutor
In regards to math, we are professionals.
Get In Touch
Email: camtutor.ai@gmail.com