Question

A larger number is 2 more than 4 times a smaller number. The larger number is also 8 more than 2 times the smaller number.

1. Define the variables: x = smaller number and y = larger number

2. Identify the key words: more than (addition), times (multiplication), is (equals)

3. Write the equations.


Which equation represents a larger number that is 2 more than 4 times a smaller number?

Which equation represents a larger number that is 8 more than 2 times a smaller number?

Answer 1

Answer:

see the explanation

Step-by-step explanation:

Let

x ----> the smaller number

y ----> the larger number

we know that

A larger number is 2 more than 4 times a smaller number

Identify the key words

is (=)---> equal

more (+) ---> addition

times (*) ---> multiplication

That means

The larger number y is equal  to multiply the smaller number x by 4 and then adds 2

so

$y=4x+2$ ----> equation A

The larger number is also 8 more than 2 times the smaller number

Identify the key words

is (=)---> equal

more (+) ---> addition

times (*) ---> multiplication

That means

The larger number y is equal  to multiply the smaller number x by 2 and then adds 8

so

$y=2x+8$ ----> equation B

Solve the system of equations by substitution

equate equation A and equation B

$4x+2=2x+8$

$4x-2x=8-2\\2x=6\\x=3$

Find the value of y

substitute the value of x in equation A or equation B

$y=4(3)+2=14$

therefore

The smaller number is 3 and the larger number is 14

Answer 2

Answer:

c and d

Step-by-step explanation:

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