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3 years ago

Enter the sum of numbers as a product of their GCF. 75 + 30 The sum of the numbers as a product of their GCF is

Mathematics

1 answer:

Oksanka [162]3 years ago

7 0

Answer: 75+30 = 15 x 7

Step-by-step explanation:

The given expression is 75+30 (=105) which defines the sum of 75 and 30.

Prime factorization of 75 and 30 are as below:

75 = 5 x 5 x 3

30 = 5 x 3 x 2

GCD (75,30) = 5x 3 = 15 [Note: GCD = Greatest common divisor]

Consider 75+30 = (15 x 5) + (15 x 2) [75 = 15 x 5 and 30= 15 x 2]

= 15 (5+2) [taking 15 as common ]

= 15 x (7)

(=105)

So, 75+30 which is sum of the numbers and it is expressed as 15 x 7 which a product of their GCF.

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Step-by-step explanation:

We can write this word problem as two variables. Let us assume that:

x = Natalie's age

y = Fred's age

The first part of the word problem is that "If you add Natalie's age and Fred's age, the result is 39." Therefore:

Natalie's age + Fred's age = 39

x + y = 39

This will be our first equation. The second equation can be derived from the statement that "If you add Fred's age to 4 times Natalie's age, the result is 78." Therefore:

(4 times Natalie's age) + Fred's age = 78

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We can now form a system of equations and solve for both x and y:

$\left \{ {{x + y = 39} \atop {4x + y = 78}} \right.$

The simplest way to solve would be using the Substitution method, as seen here:

x + y = 39

y = 39 - x

4x + y = 78

4x + (39 - x) = 78

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3x = 39

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x + y = 39

13 + y = 39

y = 26

Remember that x = Natalie's age and y = Fred's age. Therefore, Natalie's age is 13 years old and Fred's age is 26 years old.

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