At Irv's Cycle Rental Shop, Irv renst all knids of cycles: unicyles, tandem bikes, regualr bikes, and even tricycles for little kids. He parks all the cycles in front of the shop with a helmet for each rider strapped to the cycles. This morninf Irv counted 57 helments and 115 wheels parked in front of his store. He knows he has an equal number of unicycles and tandem bikes. He also knows that he has 32 regular bikes. How many unicycle, tandem bikes, and tricycles does Irv have?
THIS EASY Katherine
Uni:tandem, reg : tri
27 27 32 29
total bickes are 115-32(regualr bikes)= 83
83/3=27 R 2 (27+2 for tri)
he knows that an equal numbr of nui and tand. so 27+27=54
CHECK= 27+27+32+29=115
To solve this problem, we can set up a system of equations based on the information provided.
Let's assume the number of unicycles is "x" and the number of tandem bikes is also "x". Given that Irv has 32 regular bikes, we can represent the total number of wheels as:
1 wheel per unicycle (x wheels)
2 wheels per tandem bike (2x wheels)
2 wheels per regular bike (32 × 2 wheels)
We can now set up an equation for the total number of wheels:
x + x + 32 × 2 = 115
Simplifying this equation, we have:
2x + 64 = 115
Subtracting 64 from both sides:
2x = 115 - 64
2x = 51
Dividing both sides by 2:
x = 51 / 2
x = 25.5
Since we cannot have a fractional number of unicycles or tandem bikes, we can conclude that Irv has 25 unicycles and 25 tandem bikes.
To find the number of tricycles, we can subtract the total number of unicycles, tandem bikes, and regular bikes from the total number of helmets:
57 helmets - (25 unicycles + 25 tandem bikes + 32 regular bikes) = 57 - (25 + 25 + 32) = 57 - 82 = -25
Since it wouldn't make sense to have a negative number of tricycles, we can conclude that Irv does not have any tricycles.
In summary, Irv has 25 unicycles, 25 tandem bikes, and no tricycles.