Question

Two numbers x and y are such that:a) The sum of 3 times x and 5 times y is 57b) y is 1 more than twice the value of xWhat is the value of x +y?

Answer 1

Concept

Write two equations from the two-word problems.

a) The sum of 3 times x and 5 times y is 57

Sum means addition (+)

3 times x = 3x

5 times y = 5y

Therefore, their sum:

3x + 5y = 57 --------------------------- (1)

b) y is 1 more than twice the value of x.

'More than'Kindly means addition.

twice of x = 2x

y is 1 more than twice of x is y = 2x + 1

y = 2x + 1 ------------------------------------------- (2)

Next, solve equations 1 and 2 simultaneously to find x and y using the substitution method.

Substitute y in equation 2 into equation 1.

3x + 5y = 57

3x + 5(2x + 1) = 57

3x + 10x + 5 = 57

Collect like terms

3x + 10x = 57 - 5

13x = 52

Divide 13 on both side to get:

`\begin{gathered} (13x)/(13)\text{ = }(52)/(13) \\ x\text{ = 4} \end{gathered}`

Next, substitute x in y = 2x + 1 to find the value of y.

y = 2(4) + 1

y = 8 + 1

y = 9

=

Final answer

The value of x + y is 4 + 9 = 13

x + y = 13