Let’s solve each part step-by-step to find the unknown term [tex]\( a \)[/tex].
### Part (a)
We start with the equation:
[tex]\[ \frac{9}{a} = \frac{4}{7} \][/tex]
To solve for [tex]\( a \)[/tex], we can cross-multiply:
[tex]\[ 9 \times 7 = a \times 4 \][/tex]
[tex]\[ 63 = 4a \][/tex]
Now, divide both sides by 4 to isolate [tex]\( a \)[/tex]:
[tex]\[ a = \frac{63}{4} \][/tex]
[tex]\[ a = 15.75 \][/tex]
So, the value of [tex]\( a \)[/tex] for part (a) is:
[tex]\[ a = 15.75 \][/tex]
### Part (b)
The given equation is:
[tex]\[ a \times 4 \times 8 = 64 \][/tex]
Combine the constants on the left-hand side:
[tex]\[ a \times 32 = 64 \][/tex]
Now, divide both sides by 32 to solve for [tex]\( a \)[/tex]:
[tex]\[ a = \frac{64}{32} \][/tex]
[tex]\[ a = 2.0 \][/tex]
So, the value of [tex]\( a \)[/tex] for part (b) is:
[tex]\[ a = 2.0 \][/tex]
### Part (c)
The given equation is:
[tex]\[ (a + 50) \times 4 = 240 \][/tex]
First, divide both sides by 4 to simplify:
[tex]\[ a + 50 = \frac{240}{4} \][/tex]
[tex]\[ a + 50 = 60 \][/tex]
Next, subtract 50 from both sides to isolate [tex]\( a \)[/tex]:
[tex]\[ a = 60 - 50 \][/tex]
[tex]\[ a = 10.0 \][/tex]
So, the value of [tex]\( a \)[/tex] for part (c) is:
[tex]\[ a = 10.0 \][/tex]
### Part (d)
The given equation is:
[tex]\[ (a - 300) \times 6 = 102 \][/tex]
First, divide both sides by 6 to simplify:
[tex]\[ a - 300 = \frac{102}{6} \][/tex]
[tex]\[ a - 300 = 17 \][/tex]
Next, add 300 to both sides to isolate [tex]\( a \)[/tex]:
[tex]\[ a = 17 + 300 \][/tex]
[tex]\[ a = 317.0 \][/tex]
So, the value of [tex]\( a \)[/tex] for part (d) is:
[tex]\[ a = 317.0 \][/tex]
### Summary
The unknown term [tex]\( a \)[/tex] for each part is:
- (a) [tex]\( a = 15.75 \)[/tex]
- (b) [tex]\( a = 2.0 \)[/tex]
- (c) [tex]\( a = 10.0 \)[/tex]
- (d) [tex]\( a = 317.0 \)[/tex]
