The larger number is equal to 64 and the smaller number is equal to 36.
- Let the smaller number be x.
- Let the larger number be y.
To write the word problem as an algebraic equation:
In this exercise, we are required to translate the word problem into a mathematical (algebraic) expression and solve for the unknown variable (number):
Translating the word problem into an algebraic expression, we have;
The difference between two numbers is 28:
[tex]y-x=28[/tex] ....equation 1
The larger number is 8 less than twice the smaller number:
[tex]y=2x-8[/tex] ...equation 2
Substituting eqn 2 into eqn 1, we have:
[tex]2x-8-x=28\\\\x-8=28\\\\x=28+8[/tex]
x = 36
To find the value of y:
[tex]y=2x-8\\\\y=2(36)-8\\\\y=72-8[/tex]
y = 64
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