A climbing gym charges $10 to climb each day.A pair. of climbing charges shoes cost $84.It costs $169 to buy 6 days of climbing,one pair of climbing shoes,and one harness.How much does a harness cost? WRITE AN EQUATION FOR EACH PROBLEM. USE A VARIABLE FOR THE UNKNOWN NUMBER. SOLVE.

Respuesta :

The correct answer is:

The harness is $25.

Explanation:

Let x represent the cost of the harness.

Each day of climbing is $10. This means 6 days of climbing is represented with 10(6). The shoes are $84. This makes our expression 10(6)+84. Adding the harness, x, to that, our total comes to $169. This gives us the equation

10(6)+84+x = 169

Simplifying the left hand side, we have

60+84+x = 169

Combining like terms, we have

144+x = 169

Subtract 144 from each side:

144+x-144 = 169-144

x = 25

The harness is $25.

The equation representing the given problem is:

6x   +  y  +  z  =   169

A harness costs $25

Let the charge for 1 day of climbing be represented by x

x  =  $10

Let the price of 1 pair of climbing shoes be represented by y

y  =  $84

Let the price of 1 harness be represented by z

It costs $169 to buy 6 days of climbing, one pair of climbing shoes, and one harness

Total cost  =  $169

The equation representing the given scenario is:

6x   +  y  +  z  =   169

To find the value of z, substitute x = 10 and y = 84 into the equation

6(10)  +  84  +  z  =  169

60  +  84  +  z  =  169

144  +  z  =  169

z  =  169  -  144

z   =  25

Therefore, a harness costs $25

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