Answer :
a. The number of meters worth N25,600 is d - 18.
b. The selling price of 1 meter of cloth in terms of d is [tex]\(\frac{25,600}{d}\).[/tex]
c. The length of a full roll of cloth is 32 meters.
a. To find how many meters of cloth are worth N25,600, we need to subtract the value of the sold cloth from the total value of the full roll. Since 18 meters have been sold, the remaining length is d - 18 meters. Given that the value of the remaining cloth is N25,600, we can set up the equation:
[tex]\[ \text{Value of remaining cloth} = \text{Total value} - \text{Value of sold cloth} \]\[ 25,600 = \text{Total value} - 18 \times \text{Price per meter} \][/tex]
We are given that the value of the full roll is the same as the value of the remaining cloth:
[tex]\[ 25,600 = (d \times \text{Price per meter}) - 18 \times \text{Price per meter} \][/tex]
Now, we can solve for the price per meter.
b. To express the selling price of 1 meter of cloth in terms of d, we divide the total value of the cloth by the total length of the cloth:
[tex]\[ \text{Price per meter} = \frac{\text{Total value}}{d} \][/tex]
c. If the selling price is N800 per meter, we can use this price to find the length of a full roll of cloth. We'll set the price per meter equal to N800 and solve for d:
[tex]\[ 800 = \frac{25,600}{d} \][/tex]
Now, let's solve these equations step by step.
a.
[tex]\[ 25,600 = (d \times \text{Price per meter}) - 18 \times \text{Price per meter} \]\[ 25,600 = (d - 18) \times \text{Price per meter} \]\[ 25,600 = (d - 18) \times \frac{\text{Total value}}{d} \][/tex]
b. [tex]\[ \text{Price per meter} = \frac{\text{Total value}}{d} \][/tex]
c [tex]\[ 800 = \frac{25,600}{d} \][/tex]
Now, let's solve each equation. Starting with part a:
a. We're given that the value of the remaining cloth is N25,600 and 18 meters have been sold. So, the value of the sold cloth is [tex]\( 18 \times \text{Price per meter} \)[/tex], which we subtract from the total value to find the value of the remaining cloth.
[tex]\[ 25,600 = (d \times \text{Price per meter}) - 18 \times \text{Price per meter} \]\[ 25,600 = (d - 18) \times \text{Price per meter} \]\[ \text{Price per meter} = \frac{25,600}{d - 18} \][/tex]
b. The selling price of 1 meter of cloth in terms of d is simply the total value divided by the total length of cloth:
[tex]\[ \text{Price per meter} = \frac{\text{Total value}}{d} \]\[ \text{Price per meter} = \frac{25,600}{d} \][/tex]
c. We're given that the selling price is N800 per meter. So, we set the price per meter equal to N800 and solve for d:
[tex]\[ 800 = \frac{25,600}{d} \]\[ d = \frac{25,600}{800} \][/tex]
d = 32
So, the length of a full roll of cloth is 32 meters.
