A -gallon [gal] quantity of molten (liquefied) plastic is going to be used to make a 1-foot [ft] by 8-inch [in] plastic block. If liters [L] of the plastic is lost in the manufacturing process, how thick is the final plastic block, in units of inches [in]?

x  = 1,77 in

Step-by-step explanation:

Total volume of molten plastic to make  a block is

1 [gal] - 1 L (lost in the process)  =  3,7854 - 1  =  2,7854

Now the volume of the block is:

1 foot  * 8 inches * x ( thick of the block )

1 foot is 0,3048 meter  and 1 inch is 0,0254 meter

Then  in m³  the volume of the block is

0,3048 * 8 * 0,0254 * x  =  0,06193536 * x  [ m³ ]

That volume should be equal to  2,7854 / 1000

Therefore

 0,06193536 * x  = 2,7854 / 1000        x in m³

x = 2,7854 /61,93536  m

x  =  0,044972  m      and    1 m  =  39,37 in

x  = 1,77 in

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step-by-step explanation:

egge

ratios represent a pattern or relationship that can be scaled.

equivalent ratios are pairs of ratios that represent the same relationship between quantities, and can be generated by multiplying or dividing both quantities in the ratio by the same factor.

in this lesson, students will use double number lines and ratio reasoning to solve ratio problems. by partitioning double number lines into proportionate intervals, students will build an understanding of equivalent ratio relationships as those that are generated by multiplying or dividing two related quantities by the same number. this lesson will build upon students' prior understanding of multiplicative comparisons, number line reasoning and equivalent fractions (while highlighting the difference between equivalent fractions and equivalent ratios); and will build toward future work in this unit on building ratio tables, and work in future grades in proportionality, scaling, and expressing and graphing linear functions.

step-by-step explanation:

ratios represent a pattern or relationship that can be scaled.

equivalent ratios are pairs of ratios that represent the same relationship between quantities, and can be generated by multiplying or dividing both quantities in the ratio by the same factor.

in this lesson, students will use double number lines and ratio reasoning to solve ratio problems. by partitioning double number lines into proportionate intervals, students will build an understanding of equivalent ratio relationships as those that are generated by multiplying or dividing two related quantities by the same number. this lesson will build upon students' prior understanding of multiplicative comparisons, number line reasoning and equivalent fractions (while highlighting the difference between equivalent fractions and equivalent ratios); and will build toward future work in this unit on building ratio tables, and work in future grades in proportionality, scaling, and expressing and graphing linear functions.