Snap, Crackle and Pop went to the mall for shopping. They shopped in three different shops X, Y and Z. Snap bought two pairs of shoes, one belt and two pairs of pants at X. Crackle bought one pair of shoes, one belt, and four pairs of pants at Y. Pop bought two pairs of shoes, three belts, and one pair of pants at Z. The price of each pair of pants at shop Z was 20% more compared to other shops, while the belts and shoes were the same price across the stores. They each spent the same amount of money - R2 500. What was the price of each belt?

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answer: translate the circles so they share a common center point and dilate circle y by a scale factor of 3.

step-by-step explanation:

part a. the differences are decreasing, so we know the sequence is not arithmetic. the ratios are constant (=3/4), so we know the sequence is geometric.

part b. from part a, we know the common ratio is 3/4, so each term is 3/4 of the one before. the initial term is the number of gallons at h=1.

g[h] = (3/4)·g[h-1]

g[1] = 384 . . . . initial value required for a recursive definition

part c. the general formula for a geometric sequence is

a[n] = a[1]·r^(n-1)

we have a[1] = 384, r = 3/4, and the term number given by h. the formula that follows is

g[h] = 384·(3/4)^(h-1)

part d. filling in the value and doing the arithmetic, we have

g[12] = 384·(3/4)^11 ≈ 384·0.042235136 ≈ 16.2183 . . gallons

part e. each gallon is 4 quarts, so

16.2183 gal × 4 qt/gal = 64.8732 qt