Answer :
Sure, let's solve each part of the problem step-by-step.
### Part a:
You have the ratio [tex]\(9:2\)[/tex] and you need to find the value of [tex]\(x\)[/tex] in the ratio [tex]\(x:7\)[/tex].
1. Set up the proportion: [tex]\( \frac{9}{2} = \frac{x}{7} \)[/tex].
2. Cross-multiply to solve for [tex]\(x\)[/tex]:
[tex]\(9 \times 7 = 2 \times x\)[/tex].
3. This gives: [tex]\(63 = 2x\)[/tex].
4. Solve for [tex]\(x\)[/tex] by dividing both sides by 2:
[tex]\(x = \frac{63}{2} = 31.5\)[/tex].
So, the value of [tex]\(x\)[/tex] for part a is 31.5.
### Part b:
You have the ratio [tex]\(15:25\)[/tex] and you need to determine [tex]\(x\)[/tex] in the ratio [tex]\(3:x\)[/tex].
1. Set up the proportion: [tex]\( \frac{15}{25} = \frac{3}{x} \)[/tex].
2. Cross-multiply to solve for [tex]\(x\)[/tex]:
[tex]\(15 \times x = 25 \times 3\)[/tex].
3. This gives: [tex]\(15x = 75\)[/tex].
4. Solve for [tex]\(x\)[/tex] by dividing both sides by 15:
[tex]\(x = \frac{75}{15} = 5\)[/tex].
So, the value of [tex]\(x\)[/tex] for part b is 5.
### Part c:
You have the ratio [tex]\(16:64\)[/tex] and need to find [tex]\(x\)[/tex] for an equivalent ratio where the second term is 16.
1. Set up the proportion: [tex]\( \frac{16}{64} = \frac{x}{16} \)[/tex].
2. Cross-multiply to solve for [tex]\(x\)[/tex]:
[tex]\(16 \times 16 = 64 \times x\)[/tex].
3. This gives: [tex]\(256 = 64x\)[/tex].
4. Solve for [tex]\(x\)[/tex] by dividing both sides by 64:
[tex]\(x = \frac{256}{64} = 4\)[/tex].
The value of [tex]\(x\)[/tex] for part c is 4.
That's the step-by-step solution for each part.
### Part a:
You have the ratio [tex]\(9:2\)[/tex] and you need to find the value of [tex]\(x\)[/tex] in the ratio [tex]\(x:7\)[/tex].
1. Set up the proportion: [tex]\( \frac{9}{2} = \frac{x}{7} \)[/tex].
2. Cross-multiply to solve for [tex]\(x\)[/tex]:
[tex]\(9 \times 7 = 2 \times x\)[/tex].
3. This gives: [tex]\(63 = 2x\)[/tex].
4. Solve for [tex]\(x\)[/tex] by dividing both sides by 2:
[tex]\(x = \frac{63}{2} = 31.5\)[/tex].
So, the value of [tex]\(x\)[/tex] for part a is 31.5.
### Part b:
You have the ratio [tex]\(15:25\)[/tex] and you need to determine [tex]\(x\)[/tex] in the ratio [tex]\(3:x\)[/tex].
1. Set up the proportion: [tex]\( \frac{15}{25} = \frac{3}{x} \)[/tex].
2. Cross-multiply to solve for [tex]\(x\)[/tex]:
[tex]\(15 \times x = 25 \times 3\)[/tex].
3. This gives: [tex]\(15x = 75\)[/tex].
4. Solve for [tex]\(x\)[/tex] by dividing both sides by 15:
[tex]\(x = \frac{75}{15} = 5\)[/tex].
So, the value of [tex]\(x\)[/tex] for part b is 5.
### Part c:
You have the ratio [tex]\(16:64\)[/tex] and need to find [tex]\(x\)[/tex] for an equivalent ratio where the second term is 16.
1. Set up the proportion: [tex]\( \frac{16}{64} = \frac{x}{16} \)[/tex].
2. Cross-multiply to solve for [tex]\(x\)[/tex]:
[tex]\(16 \times 16 = 64 \times x\)[/tex].
3. This gives: [tex]\(256 = 64x\)[/tex].
4. Solve for [tex]\(x\)[/tex] by dividing both sides by 64:
[tex]\(x = \frac{256}{64} = 4\)[/tex].
The value of [tex]\(x\)[/tex] for part c is 4.
That's the step-by-step solution for each part.
