The sum of two numbers is 17. One number is 3 less than 2/3 of the other number. What is the lesser number?

Carina Nash

Carina Nash

Answered question

2023-01-18

The sum of two numbers is 17. One number is 3 less than 23 of the other number. What is the lesser number?

Answer & Explanation

mizzxrizzeui

mizzxrizzeui

Beginner2023-01-19Added 5 answers

We can write the following by dialing these fictitious numbers x and y:
x+y=17
"One number is 3 less than 2/3 of the other number," we then see.
Let's say that #y# is the "one number." If y is 3 less than 2/3 of x, this is written as:
y=23x3
From here, we have to take this equation for y and use it in our first equation. Since we know that y and 23x3 are equal, we can replace y with 23x3 in the first equation:
x+y=17
x+23x3=17
From here, we can add x+23x using fractions: x+23x=33x+23x=53x
53x3=17
Add 3 to both sides of the equation:
53x=20
Multiply both sides by 35:
x=20×35=5(4)(3)5=12
If x=12, then y=5, since their sum is 17.
So the two numbers are 5 and 12.
Enrique Cunningham

Enrique Cunningham

Beginner2023-01-20Added 1 answers

The two numbers can be defined with just one variable.
Let the smaller number be x
The other number is (17x)    (We know they add up to 17)
23 of the bigger number is written as: 23(17x)
The smaller number is 3 less than that. (so, subtract 3 to get x)
x=23(17x)3    we have an equation, solve for x
Undefined control sequence \cancel
   3x=342x9
3x+2x=25
   5x=25
   x=5
The smaller number is 5, the larger is 12
Check: 23×123=83=5

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