Answer :
To determine which among the given equations accurately represents the written description, let's break down the sentence "Seven times the difference between 35.8 and a number is equal to 53.4" into its mathematical components.
1. "Seven times" indicates a multiplication by 7.
2. "the difference between 35.8 and a number" suggests a subtraction where 35.8 is the first term and the unknown number (let's call it [tex]\( m \)[/tex]) is the second term.
3. "is equal to 53.4" translates to [tex]\( = 53.4 \)[/tex].
Combining these elements, we understand that:
1. We need to take the difference [tex]\( 35.8 - m \)[/tex].
2. Then, we multiply this difference by 7.
3. Finally, set this product equal to 53.4.
This translates mathematically to:
[tex]\[ 7 \times (35.8 - m) = 53.4 \][/tex]
Now let's compare this with the given equations:
1. [tex]\( 7(35.8) - m = 53.4 \)[/tex]
2. [tex]\( 7(35.8 - m) = 53.4 \)[/tex]
3. [tex]\( 7(m - 35.8) = 53.4 \)[/tex]
4. [tex]\( 7m - 35.8 = 53.4 \)[/tex]
The equation that matches our interpretation of the written description "Seven times the difference between 35.8 and a number is equal to 53.4" is:
[tex]\[ 7(35.8 - m) = 53.4 \][/tex]
Therefore, the correct equation is:
[tex]\[ \boxed{7(35.8 - m) = 53.4} \][/tex]
The corresponding option is the second one.
1. "Seven times" indicates a multiplication by 7.
2. "the difference between 35.8 and a number" suggests a subtraction where 35.8 is the first term and the unknown number (let's call it [tex]\( m \)[/tex]) is the second term.
3. "is equal to 53.4" translates to [tex]\( = 53.4 \)[/tex].
Combining these elements, we understand that:
1. We need to take the difference [tex]\( 35.8 - m \)[/tex].
2. Then, we multiply this difference by 7.
3. Finally, set this product equal to 53.4.
This translates mathematically to:
[tex]\[ 7 \times (35.8 - m) = 53.4 \][/tex]
Now let's compare this with the given equations:
1. [tex]\( 7(35.8) - m = 53.4 \)[/tex]
2. [tex]\( 7(35.8 - m) = 53.4 \)[/tex]
3. [tex]\( 7(m - 35.8) = 53.4 \)[/tex]
4. [tex]\( 7m - 35.8 = 53.4 \)[/tex]
The equation that matches our interpretation of the written description "Seven times the difference between 35.8 and a number is equal to 53.4" is:
[tex]\[ 7(35.8 - m) = 53.4 \][/tex]
Therefore, the correct equation is:
[tex]\[ \boxed{7(35.8 - m) = 53.4} \][/tex]
The corresponding option is the second one.
