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Write simultaneous equations to describe the situation below, solve using substitution, and fill in the blanks.

Dedra and Nick both went bowling last weekend, but not together. Dedra went during open bowling time, paying €2 for shoe rental and €3 per hour. Nick went on family night, when each hour was €1 and shoe rental was €6. As it turned out, they played for the same number of hours and spent the same amount. How many hours did each one bowl? How much did each one spend?


Dedra and Nick each bowled for 'blank' hours and spent €. 'blank'



Answer :

iGreen
Dedra:

y = 2 + 3x

Nick:

y = 6 + x

Where 'y' is the total cost, and 'x' represents the number of hours.

Solve using substitution, we can substitute 2 + 3x for 'y' in the 2nd equation.

y = 6 + x

2 + 3x = 6 + x

Subtract 2 to both sides:

3x = 4 + x

Subtract 'x' to both sides:

2x = 4

Divide 2 to both sides:

x = 2

Now we can plug this into any of the two equations to get our 'y' value.

y = 2 + 3x

y = 2 + 3(2)

y = 2 + 6

y = 8

So our full solution is (2, 8). 

Which means they both bowled for 2 hours, and spent €8.

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