Abstract number problems: One number is 5 more than....

Redeemed3:16

New member
I do not know where to begin to sovle this problem. I am homeschooled and I dont have a teacher that can walk me through it.
Can someone show me how to solve this problem, and a trick to solve others like it? I dont know how to take the words and put them in an equation. I am having difficulty in translating the words into numbers and variables to solve the problem.

One number is five more than another and their sum is three less than three times the smaller. Find the numbers.

I also need help on this problem.

Joe is 10 years older than James. In 8 years, twice Joe's age will equal three times James's age. How old is each now? :?

stapel

Super Moderator
Staff member
Redeemed3:16 said:
I do not know where to begin to sovle this problem. I am homeschooled...
If your current curriculum is leaving you entirely lost, then you might want to consider switching to something that is of higher quality. I'm afraid we simply aren't able here to replace the missing hours of instruction that you need. Sorry!

Redeemed3:16 said:
I am having difficulty in translating the words into numbers and variables to solve the problem.
To learn how to "translate" word problems, please study a few of the many great lessons available online:

. . . . .Google results for "translate word problems"

Redeemed3:16 said:
One number is five more than another and their sum is three less than three times the smaller. Find the numbers.
First, learn how the topic works:

. . . . .Google results for "number word problems"

. . . . .i) Pick a variable for "another number", since "one number" is defined
. . . . . . .in terms of "another number".

. . . . .ii) Write an expression, in terms of the variable in (i), for "one number".

. . . . .iii) Write out the sum of (i) and (ii), and simplify.

. . . . .iv) Write an expression, in terms of the "smaller" number (obviously
. . . . . . .the "another number"), for "three times the smaller".

. . . . .v) Write an expression, in terms of (iv), for "three less than" three
. . . . . . .times the smaller number.

. . . . .vi) Set (iii) equal to (v).

. . . . .vii) Solve for the variable in (i).

. . . . .viii) Back-solve for the other number, using (ii).

Redeemed3:16 said:
Joe is 10 years older than James. In 8 years, twice Joe's age will equal three times James's age. How old is each now?
First, learn how the topic works:

. . . . .Google results for "age word problems"

Then follow the process that the lessons you studied explained:

. . . . .i) Joe is defined in terms of James, so pick a variable for James'
. . . . . . .age right now.

. . . . .ii) Write an expression, in terms of (i), for Joe's age right now.

. . . . .iii) Write a new expression for James' age in eight years. (That
. . . . . . .is, add "8" to (i).)

. . . . .iv) In the same way, write a new expression for Joe's age in eight
. . . . . . .years, and simplify.

. . . . .v) Write an expression, in terms of (iv), for "twice" Joe's future
. . . . . . .age, and simplify.

. . . . .vi) Write an expression, in terms of (iii), for "three times" James'
. . . . . . .future age, and simplify.

. . . . .vii) Set (v) equal to (vi), and solve.

. . . . .viii) Back-solve, in terms of (i) and (ii), for their current ages.

If you get stuck, please reply showing how far you have gotten in following the instructions. Thank you!

Eliz.

Redeemed3:16

New member
Thank you so very much. I got the second problem, James is 12 and Joe is 22.
I am still having a problem with the first one posted though. From step one to step two there seems to be two variables. Is it substitution or elimination, that sort of thing? :?

Subhotosh Khan

Super Moderator
Staff member
Redeemed3:16 said:
One number is five more than another and their sum is three less than three times the smaller. Find the numbers.
?
Name Variable/s

Let

#1 variable = E

other (smaller) variable = R

One number is five more than another

E = R + 5 ...............................................................................(1)

their sum is three less than three times the smaller

E + R = 3R - 3..............................................................................(2)

from (1) in (2) - substitution

(R + 5) + R = 3R - 3.....................................................................(3)

Solve (3) for 'R'

then use that in (1) to solve for 'E'.

Then use these values in (1) & (2) - the given conditions - to check your values for correctness.

Redeemed3:16

New member
I am grateful for your help as well as the person who posted earlier. My homeschool stuff is not always like this. Most of the time I can figure it out, by the grace of God. However, the key only shows the answer in math, not how to get there. Normally, if I am stuck I just work backward from the key, and figure it out that way. Typically though I don't really require a key. :lol:

Okay, now I get it. E=13, R=8.

When you first started you had E=R+5.
I had the R+5 just not the E. Thank you so much. I would not have figured that out myself from the problem. Why exactly would the E be included when that part is not even mentioned in the first part? Is it suppose to be implied or something, or is there a method to the madness?

Mrspi

Senior Member
Redeemed3:16 said:
I am grateful for your help as well as the person who posted earlier. My homeschool stuff is not always like this. Most of the time I can figure it out, by the grace of God. However, the key only shows the answer in math, not how to get there. Normally, if I am stuck I just work backward from the key, and figure it out that way. Typically though I don't really require a key. :lol:

Okay, now I get it. E=13, R=8.

When you first started you had E=R+5.
I had the R+5 just not the E. Thank you so much. I would not have figured that out myself from the problem. Why exactly would the E be included when that part is not even mentioned in the first part? Is it suppose to be implied or something, or is there a method to the madness?

Actually, it IS mentioned. The problem says "one number (that's been defined as E) is (this will be where the equals sign goes) 5 more than the other number (the "other number" has been defined as R)"

So, this sentence translates into the equation E = R + 5

A key part of solving word problems is to start by defining variables to represent each "missing number," and then using those variables to translate the sentences of the problem into equations.