Question

23 inches of wire cost 92 cents at the same rate, how much (in cents) will 34 inches of wire cost?

Answer 1

Explanation:

the trick is to find the "norm" rate, which is the rate for one unit.

from there we can get the rate for any number of units just by multiplying.

so,

23 in for 92 cents.

that means the rate is

23/92 = 23/(23×4) = 1/4

so, by dividing numerator and denominator by 23 (in this case it has an integer result also for the denominator) we get the price for 1 inch of wire : 4 cents.

so, 34 inches then have the length/price ratio (we multiply numerator and denominator by 34)

1/4 × 34/34 = 34/136

that means 34 inches cost 136 cents (= $1.36).

Answer 2

Explanation:

Let's use the formula rate = cost/length to find the cost of one inch of wire. We know that 23 inches of wire cost 92 cents, so the rate of one inch of wire can be found by dividing 92 cents by 23 inches:

rate = cost/length = 92 cents/23 inches = 4 cents/inch

Now that we have found the rate of one inch of wire, we can use it to find the cost of 34 inches of wire. We simply multiply the rate by the length:

cost = rate * length = 4 cents/inch * 34 inches = 136 cents

So, 34 inches of wire will cost 136 cents.