Question

Question 5

During gym class, Kathryn did 5 times as many pushups as Grace. Together, they did a total of 42 pushups. How
many push-ups did each person do during the gym class?
Part A
Write a system of equations that represents the situation.
y=
x + y =
Part B
Solve the system of equations. Express the coordinates as decimals if necessary.

Answer 1

The number of pushups done by Grace and Kathryn is 7 and 35 respectively

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data,

Let the equation be represented as A

Now , the value of A is

Let the number of pushups by Grace be x

Let the number of pushups by Kathryn be y

Now, Kathryn did 5 times as many pushups as Grace

`y = 5x` be equation (1)

And, they did a total of 42 pushups together

`x + y = 42` be equation (2)

Substituting the value of y in the equation, we get

`x + 5x = 42`

`6x = 42`

Divide by 6 on both sides, we get

`x = 7` pushups

And,
`y = 35` pushups

So, the number of pushups by Grace is 7 and by Kathryn is 35 respectively