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How do i solve this problem?
a number is 15 more than another. the sum of twice the larger and 3 times the smaller is 182. what are the numbers?
yes my teacher has taught me but i forgot. i do that to what i find unimportant. not only that but inorder to study, we don't get notes, we get WORKSHEETS. she gave me lessons on problems like this in october i think and of course i threw all papers related to this away because of "binder checks" where my binder must be neat and rid of old work. what was i supposed to do? leave all my old math work in my room? if you took her classes (i have a double period with her) you can understand how much 80 minutes worth of worksheets is. its A LOT and i didnt plan on making a library in my room. so can i please have some help? not only for this problem, but how to solve it.
1 Answer
- Anonymous9 years agoFavorite Answer
I'm going to assume you are in some form of Algebra (Pre-Algebra or Algebra 1) course and you know what equations and variables are.
To answer these questions, you always do the following: (a) identify two variables; (b) write two equations; (c) solve.
(a) Identify Two Variables
Here "a number is 15 more than another number" tells us we have "a number" (let's call it A) and "another number" (let's call it B).
(b) Write Two Equations
So we have "A is 15 more than B".
"Is" means = and "more than" means +.
So we have "A = 15 + B".
"the sum of twice the larger and 3 times the smaller is 182" tells us we need to know which is bigger: A or B.
Since we have to add 15 to B to get A, A must be bigger.
So we have "the sum of twice A and 3 times B is 182".
"the sum of...and" means add the next two things together and "twice" means 2times.
So we have "2A + 3B = 182".
A = 15 + B and 2A + 3B = 182
(c)Solve
If A = 15 + B, then 2A + 3B = 182 is the same as 2(15 + B) + 3B = 182. [substitution]
2(15 + B) + 3B = 182
30 + 2B + 3B = 182 [distributive property]
30 + 5B = 182 [add like terms]
5B = 152 [subtraction property]
B = 30.4 [division property]
If B = 30.4, then A = 15 + B is the same as A = 30.4 + 15. So A = 45.4.
You can (and should) check these answers in both equations you wrote to make sure they are correct.