. A pen and 12 erasers cost $17.70. A pen and 15 erasers cost $20.40. How much do 6 pens cost?
Question
. A pen and 12 erasers cost 20.40. How much do 6 pens cost?
Solution
Sure, let's solve this step by step:
Step 1: Let's denote the cost of a pen as P and the cost of an eraser as E. From the problem, we have two equations:
P + 12E = 17.70 ...(equation 1)
P + 15E = 20.40 ...(equation 2)
Step 2: To find the cost of each item, we can subtract equation 1 from equation 2. This will give us:
15E - 12E = 20.40 - 17.70
3E = 2.70
So, E = 2.70 / 3 = $0.90 (This is the cost of one eraser)
Step 3: Now, we can substitute E = $0.90 into equation 1 to find the cost of a pen:
P + 12*0.90 = 17.70
P + 10.80 = 17.70
So, P = 17.70 - 10.80 = $6.90 (This is the cost of one pen)
Step 4: Finally, to find the cost of 6 pens, we multiply the cost of one pen by 6:
6 * 41.40
So, 6 pens cost $41.40.
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