Cut 25 into two pieces in such a way that the first piece is 13 less than the second one. let x be the second one.

First piece: 6,5

Second piece: 19,5

Step-by-step explanation:

"Cut 25 into 2 pieces" = "divide 25 by 2"

So, we must divide 25 into 2 unequal pieces, where the first piece is 13 less than the second one (x).

What we could do is simply get a random number, preferably close to 12,5 (the half of 25), and add a number to the first piece and decrease a number from the second one; these two numbers, though, must add to 13 (or any other number you choose) together.

25 / 2 = 12,5

12,5 - 6 = 6,5 (this would be x - 13)

12,5 + 7 = 19,5 (this would be x)

19,5 - 6,5 = 13 or x - (x - 13) = 13 (there is indeed a difference of 13).

Hope it helped,

BiologiaMagister

For this case we propose a system of equations:

x: Variable that represents part number two

y: Variable representing part number one

According to the data we have to:

Substituting the second equation into the first we have:

Thus, the first piece measures 19 units

Thus, the second measures 6 units

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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.