High School

Which equations correctly represent the statement shown?

The value of 81 is 19 more than [tex]$j$[/tex].

A. [tex]81 = j + 19[/tex]
B. [tex]81 = j - 19[/tex]
C. [tex]19 + j = 81[/tex]
D. [tex]19 \times j = 81[/tex]
E. [tex]81 \times j = 19[/tex]
F. [tex]81 \div j = 19[/tex]

Answer :

Let's solve the problem step by step to find out which equations correctly represent the statement:

The statement is:
"The value of 81 is 19 more than [tex]\( j \)[/tex]."

This can be translated into an equation format. When the statement says that 81 is 19 more than [tex]\( j \)[/tex], it means that if we take [tex]\( j \)[/tex] and add 19 to it, we will get 81.

This forms the equation:
[tex]\[ j + 19 = 81 \][/tex]

Let's compare this with the options given:

1. [tex]\( 81 = j - 19 \)[/tex]
This implies that 81 is equal to [tex]\( j \)[/tex] minus 19. It does not match the statement that 81 is 19 more than [tex]\( j \)[/tex].

2. [tex]\( 81 = j + 19 \)[/tex]
This implies that 81 is 19 more than [tex]\( j \)[/tex]. This correctly represents the statement.

3. [tex]\( 19 + j = 81 \)[/tex]
This is a rearrangement of the equation [tex]\( j + 19 = 81 \)[/tex] and also correctly represents the statement.

4. [tex]\( 19 \times j = 81 \)[/tex]
This suggests multiplying [tex]\( j \)[/tex] by 19 equals 81, which does not match the statement.

5. [tex]\( 81 \times j = 19 \)[/tex]
This suggests multiplying [tex]\( j \)[/tex] by 81 equals 19, which does not match the statement.

6. [tex]\( 81 \div j = 19 \)[/tex]
This implies dividing 81 by [tex]\( j \)[/tex] equals 19, which does not match the statement.

Based on this analysis, the equations that correctly represent the statement "The value of 81 is 19 more than [tex]\( j \)[/tex]" are:

- [tex]\( 81 = j + 19 \)[/tex]
- [tex]\( 19 + j = 81 \)[/tex]

These equations accurately reflect the relationship described in the statement.