there were 360 coupons sold during a school carnival. the coupon prices were $8,$10 and $12and the total income from the coupon sales was $3500. the combined number of $8 and $10 coupons sold was five times the number of $12 coupons sold. find the number of coupons of each type sold

See below (I hope this helps!)

Step-by-step explanation:

Let's call the number of $8, $10 and $12 as x, y and z respectively. Then, we can write the following system:

x + y + z = 360 (1)

8x + 10y + 12z = 3500 (2)

x + y = 5z (3)

5z + z = 360 (Substitute (3) into (1))

6z = 360

z = 60

x + y = 5 * 60 (Substitute z = 60 into (3))

x + y = 300 (4)

8x + 10y + 12 * 60 = 3500 (Substitute z = 60 into (2))

8x + 10y = 2780 (5)

8x + 8y = 2400 (6) -- (Multiply (4) by 8)

2y = 380 (Subtract (6) from (5))

y = 190

x + 190 = 300 (Substitute y = 190 into (4))

x = 110

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