A credit card company offers a cash back program on transactions. For every transaction over $100 the customer gets $3 back. For every transaction $100 or less, the customer gets $1 back. The customer made 25 transactions in all and the total number of dollars given back was $29. Write and solve a system of equations to find the number of transactions of each type.

Question

Mathematics

Xavier Carney

19 January, 03:08

A credit card company offers a cash back program on transactions. For every transaction over $100 the customer gets $3 back. For every transaction $100 or less, the customer gets $1 back. The customer made 25 transactions in all and the total number of dollars given back was $29. Write and solve a system of equations to find the number of transactions of each type.

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Answers (2)

Know the Answer?

Ronnie Yu · Answer 1

X=over 100

y=100 or less

x+y=25

3x+1y=29

sole

mltiply first equation by - 1 and add to other equation

-1x-1y=-25

3x+1y=29 +

2x+0y=4

2x=4

divide by 2

x=2

sub back

x+y=25

2+y=25

minus 2

y=23

there were 2 transactions more than 100

there were 23 transactions 100 or less

Milo Cooke · Answer 2

The first equation is $3 times 9 = $27 the next equation iis $1 times 2 = $1

So you do 9 transactions over $100 and 2 transactions of $100 or lower.