14 metres of rope costs €9.52. If Joe bought 21 metres, how much change out of €20.00 do Joe get? Is there a shorter way of doing this other than dividing, multiplying and then subtracting?
Not that I know about.
To find out how much change Joe will get, we can calculate the cost of 21 meters of rope and subtract it from €20.00.
First, we need to find the cost of 1 meter of rope. We know that 14 metres of rope cost €9.52. So, we can find the cost of 1 meter by dividing the total cost by the total length: €9.52 / 14 = €0.68/m.
Next, we calculate the cost of 21 meters of rope by multiplying the cost per meter by the length: €0.68/m × 21 m = €14.28.
To find out how much change Joe gets, we subtract the cost of the rope from the amount Joe gave: €20.00 - €14.28 = €5.72.
Therefore, Joe will get €5.72 change out of €20.00.
As for a shorter way of doing this calculation, the approach mentioned above is a straightforward method to find the answer. However, you can avoid some of the intermediate steps by using proportions or ratios. Here's how:
Let's set up a proportion to compare the cost of 14 meters with €9.52 to the cost of 21 meters, which is unknown.
14 meters / €9.52 = 21 meters / x
To solve for x, cross-multiply:
14 × x = €9.52 × 21
Divide both sides by 14 to isolate x:
x = (€9.52 × 21) / 14 = €14.28
Then, subtract €14.28 from €20.00 to find the change:
€20.00 - €14.28 = €5.72
So, using proportions allows you to calculate the answer directly without intermediate steps.