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In right triangle ABC with B = 90 , we have 2 sin A = 5 cos A. What is tan A?

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2(sinA) = 5(cosA)

sinA = 2.5(cosA)

We know that  (sinA)² + (cosA)² = 1

x² + (x / 2.5)² = 1 

x = 0.92847669                (x = sinA)

cosA = x / 2.5 = 0.371390676

Angle A = 68.19859051º

tanA = sinA / cosA  

Adults => A          Boys => B            Girls => G

A + B + G => x

A = 1/4x  

B + G = 3/4          B : G = 4 : 11           (3/4) / 15 = 1/20

A = 5/20x

B = 4/20x

G = 11/20x

3(5x/20) + 4(4x/20) + 5(11x/20) = 1462

x = 340

Adults = 1/4(340) = 85 

Boys = 68

Girls = 187

In ms E's park 1/3 of the total birds were grey in color while the rest were either black or white. The white birds were twice as many as the black birds. After Ms E bought another 8 white birds and 8 black birds. The ratio of the number of white birds to the number of grey birds became 3:2. How many black birds did Ms E have in the end?

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All birds => x

Grey => x/3  or  3x/9

Black => 2x/9

White => 4x/9

Ratio      W : G = 4 : 3     (Before 8 white birds were added)

New ratio =>         (4x/9 + 8) / (3x/9) = 3 / 2        x = 144

Black birds =>     2x/9 + 8 = 40

There are some caps in a shop. 2/9 of the caps are red, 1/3 of the caps are yellow and the rest are blue. There are 436 more blue caps than red caps. How many caps are there in the shop?

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All caps => x

Red caps => 2x/9

Yellow caps => x/3  or   3x/9

Blue caps =>  x - 5x/9 = 4x/9

Caps in the shop =>   2x/9 = 4x/9 - 436    x = 1962

Ali, Benny, and Charles had 255 stamps altogether. Ali gave 3/8 of his stamps to Benny and 1/5 of them to Charles. After that, all the three boys had the same number of stamps. How many more stamps did Charles have than Benny at first?

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A + B + C = 255

Ali's stamps => x

x - (3x/8 + x/5) = 85

x = 200       (Ali's stamps at first)

3x/8 = 75     (Ali gave to Benny)

Benny had 10 stamps at first.

x/5 = 40       (Ali gave to Charles)

Charles had 45 stamps at first.

Charles had 35 more stamps than Benny!

Calvin and Susie had some game cards at first. Calvin gave 1/4 of his cards to Susie. After that, Susie gave 1/5 of her cards to Calvin. In the end, Calvin had 45 cards and Susie had 36 cards. How many cards did Calvin have at first?

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Calvin's cards => x     Susie's cards =>  y            (At first)

x + y = 81

x = 81 - y             

1/4(81 - y)        Susie received from Calvin

1/5[y + 1/4(81 - y)]           Susie gave to Calvin

4/5[y + 1/4(81 - y)] = 36          y = 33

x = 81 - 33

x = 48        Cards that Calvin had at first.

https://web2.0calc.com/questions/3-questions-on-algebra_1

Aaron, Bob, and Carl sold pies at a funfair. Aaron sold 5/8 of the total number of

pies. Bob sold 5/6 of the remaining pies and Carl sold the rest. Aaron sold 1287

more pies than Carl.

 a)       How many pies did Bob sell?

b)       How many pies did they sell altogether?

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Total number of pies => x

Aaron sold = 5/8(x)             Bob sold = 5/6(3x/8)             Carl sold = 1/6(3x/8)

"Aaron sold 1287 pies more than Carl."

5x/8 - 1/6(3x/8) = 1287  

x = 2288           (Number of pies they sold altogether)

Bob sold =>         5/6(3x/8) = 715 pies

D is on side BC of triangle ABC. We know ABC ~ ACD and angle A = 49 degrees. If BC = CD, what is angle B in degrees?

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Triangle ABC =>     ∠A = 49º,  ∠B = 41º,  ∠C = 90º

Triangle ACD =>     ∠A = 41º,  ∠C = 90º,  ∠D = 49º

These two triangles are similar!!!

Sharon sold 3/10 of her mangoes and Ahmad sold 1/4 of his.

They found that each of them had sold the same number of mangoes.

If Sharon had 36 fewer mangoes than Ahmad at first, how many mangoes did

Ahmad have left?

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Sharon had => x                             Ahmad had => x + 36

Sharon sold => 3/10(x)                   Ahmad sold => 1/4(x + 36)

3x/10 = 1/4(x + 36)          x = 180

Ahmad had left =>       3/4(x + 36) = 162