Word Problems systems

Question

In the back stockroom at the Wheel Shop, the number of seats and horns equals the number of wheels. The number of seats and handlebars equals the number of horns. Twice the number of wheels is equal to three times the number of handlebars. There are 12 wheels.

Answer 1

Lets have S represent seats, H be horns, B be handlebars, and W be wheels. Now we can create equations for each sentence in the word problem.

(Equation 1) S + H = W

(Equation 2) S + B = H

(Equation 3) 2W = 3B

(Equation 4) W = 12

Since we know from Equation 4 that W is 12, we can plug this directly into Equation 3 to get the number of handlebars, B.

2W = 3B

2(12) = 3B

24 = 3B

(divide both sides by 3)

8 = B

Now we have W and B, which we can plug into Equations 1 and 2, to get:

S + H = 12

S + 8 = H

Let's use the subtraction method for these two equations to eliminate S and solve for H.

(S+H) - (S + 8) = (12) - (H)

(simplify)

H - 8 = 12 - H

(add 8 to both sides, and add H to both sides)

2H = 20

(divide by 2)

H = 10

Now plug H = 10 into either Equation 1 or 2. We will use Equation 1.

S + H = W

S + 10 = 12

S = 2.

There are 2 seats (S), 10 horns (H), 8 handlebars (B), and 12 wheels (W).