The sum of two numbers is 32. One number is 1/3 of the other number. What are the numbers?

How to solve an algebra word problem using a 2 variable system of linear equations.

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TC Math Notes

[mitchmarkin]

Solve for the smaller number. Then no fractions to deal with.
x + 3x = 32
4x = 32
x = 8
Therefore the bigger number is 3 x 8 = 24

[dwainblackwelder]

I went directly to the equation X/3 + X = 32. Multiply both sides by 3 and you get X + 3X = 96. Combine the left side variables and you get 4x = 96. Divided both sides by 4 and x = 24. 1/3 of x = 8. Answer is 8 and 24.

[cadfael]

Jeez. Anyone forget their 8times table? Some crazy comments but it is simple.

[antichrist_revealed]

I believe the answer to this problem is in this equation: 77 - 69 = 8. When divided by 8, 32 becomes 4. Thus 3 x 4 = 12, but sense there is more to gain because we have to find 2 numbers, we double that to 24. The end result is 8 and 24.

[danielmadden]

The answer is achieved drawing rectangle with sides 3x by x, since this gives perimeter of 64, divide by8 to get x, then multiply by 3 to get 24.24 + 8 gives 32.

[hbplays]

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[FBIcriminals]

8 and 24... Duh.
Shapes and colors tomorrow?

[edwellmusonda]

One number is 1/3 of the other so that means the one number is 3X bigger than the other. That’s the same as 1/4 and 3/4 so 32/4 is 8. 8x3 is 24. 24+8=32. Boom

[rogerdudra]

Greetings from the BIG SKY. Algebra is fun.

[chrisk.]

Simple and easy, could be calculated in 5 sek just in memory.

[danielcase]

And most of it sitting in highway traffic!

[Vipre-]

I imagine the 1/3 is where many would trip up.

[tomtke]

convert words to equations
note there are two equations
There are two numbers: A and B
Eq#1:
sum is 32
A + B = 32
Eq#2:
One number is 1/3rd the other
A = 1/3B
Solve two equations in two unknowns:
A + B = 32 (Eq1)
A = 1/3B (Eq2)
Substitute 2 into 1
1/3B + B = 32 (Eq3)
4/3B = 32
B = 3/4 × 32
= 24
Solve for A:
A + B = 32 (Eq1)
A + 24 = 32
A = 8

Verify:
Eq1: A + B = 32
8 + 24 = ?32?
=32 ✔️
Eq2: A = 1/3B
8 = ?1/3 × 24?
= 8 ✔️

If YOU were designing a bridge carrying thousands of cars and trucks a day wouldn't you CHECK your answers?

[larrydickenson]

Don’t take 15 minutes to tell us they are 8 and 24?

[argonwheatbelly]

24 and 8 in about eight seconds in my head. Sorry it took so long.

⅓ + 1 = 4/3
Divide 32 by 4; that's 8.
Multiply by 3; that's 24.
Poof: 24 and 8 qed

[danielcase]

What is the cost of me maintaining my vehicle for one year?