toby's piggy bank contains only 5c and 10c coins. if it contains 65 coins with a total value of $3.80, find the
number of each type of coin.
let x and y be the number of 5c and 10c coins respectively.
use the fact that the total number of coins is 65 to set up equation 1.
write the equation in the form ax + by = c, where a is positive.

I'm not sure if it only wants you to find Equation 1 or go further and solve:

x = the number of 5c coins

y = the number of 10c coins

Equation 1: the total number of coins is 65

x + y = 65

total value of $3.80

0.05x + 0.1y = 3.8

Simultaneous Equations

Make one coefficient the same

10 * (0.05x + 0.1y = 3.80 = 0.5x + y = 38

x + y = 65

0.5x + y = 38

Subtract the equations

(x + y) - (0.5x + y)= 65 - 38

(x - 0.5x) + (y - y) = 65 - 38

0.5x = 27

x = 54

Substitute it into the original equation to find y.

x + y = 65

54 + y = 56

y = 65 - 54 = 11

Substitute it into the other equation to check it's right.

0.05x + 0.1y = 3.8

0.05(54) + 0.1(65) = 3.8

x = 54 5c coins

y = 11 10c coins

the correct option is 2.

step-by-step explanation:

according to the given information triangle abc is a right angle triangle with right angle at a. segment ab is 5 and segment ac is 7. point d is on segment bc and angles adb and adc are right angles.

it is given that triangles abd, cad, and cba are similar.

two triangles are similar if their corresponding sides are proportional.

in triangle cba, using pythagoras theorem

                      )

triangle abd and cba are similar,

                            (2)

triangle cad and cba are similar,

                      )

using (1), (2) and (3), we get

hence proved.

therefore option 2 is correct.