Problem: in cliff ’ s impressive rock collection , there are half as many igneous rocks as sedimentary rocks . of the igneous rocks , 4 / 5 are shiny and the rest are matte , while 1 / 5 of the sedimentary rocks are shiny . if there are 40 shiny igneous rocks , how many total rocks does cliff have ?
Rationale: "we can start with the known quantity and then go on to find the others . shiny igneous ricks are 40 . these are ( 4 / 5 ) of total igneous rocks . ( 4 / 5 ) * total igneous rocks = 40 total igneous rocks = 40 * ( 5 / 4 ) = 50 total sedimentary rocks = 2 * total igneous rocks = 2 * 50 = 100 total number of rocks = 50 + 100 = 150 answer ( b )"
annotated_formula: divide(multiply(divide(multiply(multiply(4, 5), 40), 4), 5), 4)