Explanation required please: x/40 = y remainder 3, x/7 = y remainder 5, if x > 70

[APlusMath]

I am assisting with advanced mental calculation classes, and have found a question that was answered, but the calculation on how to get answers to these types of questions we could not figure out.

x/40=y remainder 3
and
x/7=y remainder 5
if
x > 70

Any help is greatly appreciated.

 

[APlusMath]

I am assisting with advanced mental calculation classes, and have found a question that was answered, but the calculation on how to get answers to these types of questions we could not figure out.

x/40=y remainder 3
and
x/7=y remainder 5
if
x > 70

Any help is greatly appreciated.

EDIT
x/40=y remainder 3
and
x/7=z remainder 5
if
x > 70
what is the value of x

 

[blamocur]

I would apply the definition of integer division with reminders to both statements.

 

[Steven G]

EDIT
x/40=y remainder 3
and
x/7=z remainder 5
if
x > 70
what is the value of x

I suspect that the z should be a y

Look at this example: 29/4 = 7 remainder 1. This means that 29 = 4*7 + 1

 

[Dr.Peterson]

EDIT
x/40=y remainder 3
and
x/7=z remainder 5
if
x > 70
what is the value of x

Do you know anything about Diophantine equations? There is a standard way to solve this.

You need to find integers y and z so that 40y + 3 = 7z + 5.

 

[APlusMath]

I suspect that the z should be a y

Look at this example: 29/4 = 7 remainder 1. This means that 29 = 4*7 + 1

No the z cannot be y, then they would have to be the same number and they wont be.

 

[APlusMath]

Do you know anything about Diophantine equations? There is a standard way to solve this.

You need to find integers y and z so that 40y + 3 = 7z + 5.

Thank you I will read into that more.