19. the perimeter of a rectangle is 154 inches. the length exceeds the width by 67 inches.?

Question

find the length and the width?

20. the Everton college store paid $1496 for and order of 44 calculators. the store paid $9 for each scientific calculator. the others, all graphing calculators, cost the store $53 each. how many of each type of calculator was ordered?

21.snookers lumber can convert logos into either lumber or plywood. in a given day, the mill turns out three times as many units of plywood as lumber. it makes a profit of $20 on a unit of lumber and $40 on a unit of plywood. how many of each unit must be produced and sold in order to make a profit of $14280?
snookers lumber must produce and sell__units of lumber and __units of plywood to make a profit of $14280.

KeplJoey · Accepted Answer

19/. If we call W the width of the rectangle and L the length, then the perimeter of any rectangle is 2W + 2L. So 2L + 2W = 154. And the length exceeds the width by 67 inches, which tells us L = W + 67. Substituting into the other equation gives
2(W + 67) + 2W = 154. Expanding out the brackets gives
2W + 134 + 2W = 154, which simplifies to 4W = 20, or W = 5. And L = W + 67 = 5 + 67 = 72.
So the length is 72 inches and the width is 5 inches.



20/. Let x be the number of scientific calculators and y be the number of graphing calculators. 
The total must be 44 calculators. So x + y = 44.

Also the amount of dollars spent on scientific calculators is 9x. And the amount of dollars spent on the graphing calculators is 53y. The total spent is 1496 dollars. So 9x + 53y = 1496.

From the first equation, x = 44 - y. Substituting into the other equation gives
9(44 - y) + 53y = 1496 and expanding out the brackets gives
396 - 9y + 53y = 1496, which simplifies to
44y = 1100, and therefore 
y = 25. Also x = 44 - y = 44 - 25 = 19.

So there are 19 scientific calculators and 25 graphics calculators bought.



21/. Let x be the number of units of lumber and y be the number of units of plywood.
"Three times as many units of plywood as lumber" tells us y = 3x.

The amount of dollars of profit of lumber is 20x. The amount of dollars of profit of plywood is 40y. The amount of dollars in profit in total is 14280 dollars. So 20x + 40y = 14280, and dividing through by 20 gives x + 2y = 714, and substituting in y = 3x gives x + 2(3x) = 714, which simplifies to x + 6x = 714, or 7x = 714 and therefore x = 102. Also y = 3x = 3*102 = 306. So there are 102 units of lumber sold and 306 units of plywood sold.

malara · Answer

anticipate width is x inch then length is (x+seventy 5) inch now in accordance to the above condition 2(x+x+seventy 5)=182 2x+seventy 5=ninety one 2x=sixteen x=8 consequently width is 8 inches and length is 8+seventy 5=80 3 inches

19. the perimeter of a rectangle is 154 inches. the length exceeds the width by 67 inches.?

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